Exercise 5.1 Page: 101

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NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesExercise 5.1Page: 1011. Find the complement of each of the following angles:(i)Solution:Two angles are said to be complementary if the sum of their measures is 90o.The given angle is 20oLet the measure of its complement be xo.Then, x 20o 90o x 90o – 20o x 70oHence, the complement of the given angle measures 70o.(ii)Solution:Two angles are said to be complementary if the sum of their measures is 90o.The given angle is 63oLet the measure of its complement be xo.Then, x 63o 90o x 90o – 63o x 27oHence, the complement of the given angle measures 27o.(iii)

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesSolution:Two angles are said to be complementary if the sum of their measures is 90o.The given angle is 57oLet the measure of its complement be xo.Then, x 57o 90o x 90o – 57o x 33oHence, the complement of the given angle measures 33o.2. Find the supplement of each of the following angles:(i)Solution:Two angles are said to be supplementary if the sum of their measures is 180o.The given angle is 105oLet the measure of its supplement be xo.Then, x 105o 180o x 180o – 105o x 75oHence, the supplement of the given angle measures 75o.(ii)Solution:Two angles are said to be supplementary if the sum of their measures is 180o.The given angle is 87oLet the measure of its supplement be xo.Then,

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles x 87o 180o x 180o – 87o x 93oHence, the supplement of the given angle measures 93o.(iii)Solution:Two angles are said to be supplementary if the sum of their measures is 180o.The given angle is 154oLet the measure of its supplement be xo.Then, x 154o 180o x 180o – 154o x 26oHence, the supplement of the given angle measures 93o.3. Identify which of the following pairs of angles are complementary and which aresupplementary.(i) 65o, 115oSolution:We have to find the sum of given angles to identify whether the angles arecomplementary or supplementary.Then, 65o 115o 180oIf the sum of two angle measures is 180o, then the two angles are said to besupplementary. These angles are supplementary angles.(ii) 63o, 27oSolution:We have to find the sum of given angles to identify whether the angles arecomplementary or supplementary.Then, 63o 27o

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles 90oIf the sum of two angle measures is 90o, then the two angles are said to becomplementary. These angles are complementary angles.(iii) 112o, 68oSolution:We have to find the sum of given angles to identify whether the angles arecomplementary or supplementary.Then, 112o 68o 180oIf the sum of two angle measures is 180o, then the two angles are said to besupplementary. These angles are supplementary angles.(iv) 130o, 50oSolution:We have to find the sum of given angles to identify whether the angles arecomplementary or supplementary.Then, 130o 50o 180oIf the sum of two angle measures is 180o, then the two angles are said to besupplementary. These angles are supplementary angles.(v) 45o, 45oSolution:We have to find the sum of given angles to identify whether the angles arecomplementary or supplementary.Then, 45o 45o 90oIf the sum of two angle measures is 90o, then the two angles are said to becomplementary. These angles are complementary angles.

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles(vi) 80o, 10oSolution:We have to find the sum of given angles to identify whether the angles arecomplementary or supplementary.Then, 80o 10o 90oIf the sum of two angle measures is 90o, then the two angles are said to becomplementary. These angles are complementary angles.4. Find the angles which is equal to its complement.Solution:Let the measure of the required angle be xo.We know that, sum of measures of complementary angle pair is 90o.Then, x x 90o 2x 90o x 90/2 x 45oHence, the required angle measures is 45o.5. Find the angles which is equal to its supplement.Solution:Let the measure of the required angle be xo.We know that, sum of measures of supplementary angle pair is 180o.Then, x x 180o 2x 180o x 180/2 x 90oHence, the required angle measures is 90o.6. In the given figure, 1 and 2 are supplementary angles. If 1 is decreased, whatchanges should take place in 2 so that both angles still remain supplementary.

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesSolution:From the question, it is given that, 1 and 2 are supplementary angles.If 1 is decreased, then 2 must be increased by the same value. Hence, this angle pairremains supplementary.7. Can two angles be supplementary if both of them are:(i). Acute?Solution:No. If two angles are acute, means less than 90o, the two angles cannot besupplementary. Because, their sum will be always less than 90o.(ii). Obtuse?Solution:No. If two angles are obtuse, means more than 90o, the two angles cannot besupplementary. Because, their sum will be always more than 180o.(iii). Right?Solution:Yes. If two angles are right, means both measures 90o, then two angles can form asupplementary pair. 90o 90o 1808. An angle is greater than 45o. Is its complementary angle greater than 45o or equal to45o or less than 45o?Solution:Let us assume the complementary angles be p and q,We know that, sum of measures of complementary angle pair is 90o.Then, p q 90oIt is given in the question that p 45oAdding q on both the sides,

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles p q 45o q 90o 45o q 90o – 45o q q 45oHence, its complementary angle is less than 45o.9. In the adjoining figure:(i) Is 1 adjacent to 2?Solution:By observing the figure we came to conclude that,Yes, as 1 and 2 having a common vertex i.e. O and a common arm OC.Their non-common arms OA and OE are on both the side of common arm.(ii) Is AOC adjacent to AOE?Solution:By observing the figure, we came to conclude that,No, since they are having a common vertex O and common arm OA.But, they have no non-common arms on both the side of the common arm.(iii) Do COE and EOD form a linear pair?Solution:By observing the figure, we came to conclude that,Yes, as COE and EOD having a common vertex i.e. O and a common arm OE.Their non-common arms OC and OD are on both the side of common arm.(iv) Are BOD and DOA supplementary?Solution:-

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesBy observing the figure, we came to conclude that,Yes, as BOD and DOA having a common vertex i.e. O and a common arm OE.Their non-common arms OA and OB are opposite to each other.(v) Is 1 vertically opposite to 4?Solution:Yes, 1 and 2 are formed by the intersection of two straight lines AB and CD.(vi) What is the vertically opposite angle of 5?Solution: COB is the vertically opposite angle of 5. Because these two angles are formed by theintersection of two straight lines AB and CD.10. Indicate which pairs of angles are:(i) Vertically opposite angles.Solution:By observing the figure we can say that, 1 and 4, 5 and 2 3 are vertically opposite angles. Because these two angles areformed by the intersection of two straight lines.(ii) Linear pairs.Solution:By observing the figure we can say that, 1 and 5, 5 and 4 as these are having a common vertex and also having non commonarms opposite to each other.11. In the following figure, is 1 adjacent to 2? Give reasons.

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesSolution: 1 and 2 are not adjacent angles. Because, they are not lie on the same vertex.12. Find the values of the angles x, y, and z in each of the following:(i)Solution: x 55o, because vertically opposite angles. x y 180o [ linear pair]oo 55 y 180 y 180o – 55o y 125oThen, y z [ vertically opposite angles]o z 125(ii)

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesSolution: z 40o, because vertically opposite angles. y z 180o [ linear pair]oo y 40 180 y 180o – 40o y 140oThen, 40 x 25 180o [ angles on straight line]o65 x 180 x 180o - 65 x 115o13. Fill in the blanks:(i) If two angles are complementary, then the sum of their measures is .Solution:If two angles are complementary, then the sum of their measures is 90o.(ii) If two angles are supplementary, then the sum of their measures is .Solution:If two angles are supplementary, then the sum of their measures is 180o.(iii) Two angles forming a linear pair are .Solution:Two angles forming a linear pair are Supplementary.(iv) If two adjacent angles are supplementary, they form a .Solution:If two adjacent angles are supplementary, they form a linear pair.(v) If two lines intersect at a point, then the vertically opposite angles are always.Solution:If two lines intersect at a point, then the vertically opposite angles are always equal.(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acuteangles, then the other pair of vertically opposite angles are .Solution:If two lines intersect at a point, and if one pair of vertically opposite angles are acute

NCERT Solutions for Class 7 Maths Chapter 5Lines and Anglesangles, then the other pair of vertically opposite angles are Obtuse angles.14. In the adjoining figure, name the following pairs of angles.(i) Obtuse vertically opposite anglesSolution: AOD and BOC are obtuse vertically opposite angles in the given figure.(ii) Adjacent complementary anglesSolution: EOA and AOB are adjacent complementary angles in the given figure.(iii) Equal supplementary anglesSolution: EOB and EOD are the equal supplementary angles in the given figure.(iv) Unequal supplementary anglesSolution: EOA and EOC are the unequal supplementary angles in the given figure.(v) Adjacent angles that do not form a linear pairSolution: AOB and AOE, AOE and EOD, EOD and COD are the adjacent angles that do notform a linear pair in the given figure.

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesExercise 5.2Page: 1101. State the property that is used in each of the following statements?(i) If a b, then 1 5.Solution:Corresponding angles property is used in the above statement.(ii) If 4 6, then a b.Solution:Alternate interior angles property is used in the above statement.(iii) If 4 5 180o, then a b.Solution:Interior angles on the same side of transversal are supplementary.2. In the adjoining figure, identify(i) The pairs of corresponding angles.Solution:By observing the figure, the pairs of corresponding angle are, 1 and 5, 4 and 8, 2 and 6, 3 and 7

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles(ii) The pairs of alternate interior angles.Solution:By observing the figure, the pairs of alternate interior angle are, 2 and 8, 3 and 5(iii) The pairs of interior angles on the same side of the transversal.Solution:By observing the figure, the pairs of interior angles on the same side of the transversalare 2 and 5, 3 and 8(iv) The vertically opposite angles.Solution:By observing the figure, the vertically opposite angles are, 1 and 3, 5 and 7, 2 and 4, 6 and 83. In the adjoining figure, p q. Find the unknown angles.Solution:By observing the figure, d 125o [ corresponding angles]We know that, Linear pair is the sum of adjacent angles is 180oThen, e 125o 180o [Linear pair]oo e 180 – 125 e 55oFrom the rule of vertically opposite angles, f e 55o b d 125oBy the property of corresponding angles, c f 55o

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles a e 55o4. Find the value of x in each of the following figures if l m.(i)Solution:Let us assume other angle on the line m be y,Then,By the property of corresponding angles, y 110oWe know that Linear pair is the sum of adjacent angles is 180oThen, x y 180o x 110o 180o x 180o – 110o x 70o

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles(ii)Solution:By the property of corresponding angles, x 100o5. In the given figure, the arms of two angles are parallel.If ABC 70o, then find(i) DGC(ii) DEFSolution:(i) Let us consider that AB DGBC is the transversal line intersecting AB and DGBy the property of corresponding angles, DGC ABCThen, DGC 70o(ii) Let us consider that BC EFDE is the transversal line intersecting BC and EF

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesBy the property of corresponding angles, DEF DGCThen, DEF 70o6. In the given figures below, decide whether l is parallel to m.(i)Solution:Let us consider the two lines l and m,n is the transversal line intersecting l and m.We know that the sum of interior angles on the same side of transversal is 180o.Then, 126o 44o 170oBut, the sum of interior angles on the same side of transversal is not equal to 180o.So, line l is not parallel to line m.(ii)Solution:Let us assume x be the vertically opposite angle formed due to the intersection of thestraight line l and transversal n,

NCERT Solutions for Class 7 Maths Chapter 5Lines and AnglesThen, x 75oLet us consider the two lines l and m,n is the transversal line intersecting l and m.We know that the sum of interior angles on the same side of transversal is 180o.Then, 75o 75o 150oBut, the sum of interior angles on the same side of transversal is not equal to 180o.So, line l is not parallel to line m.(iii)Solution:Let us assume x be the vertically opposite angle formed due to the intersection of theStraight line l and transversal line n,Let us consider the two lines l and m,

NCERT Solutions for Class 7 Maths Chapter 5Lines and Anglesn is the transversal line intersecting l and m.We know that the sum of interior angles on the same side of transversal is 180o.Then, 123o x 123o 57o 180o The sum of interior angles on the same side of transversal is equal to 180o.So, line l is parallel to line m.(iv)Solution:Let us assume x be the angle formed due to the intersection of the Straight line l andtransversal line n,We know that Linear pair is the sum of adjacent angles is equal to 180o. x 98o 180o x 180o – 98o x 82oNow, we consider x and 72o are the corresponding angles.For l and m to be parallel to each other, corresponding angles should be equal.But, in the given figure corresponding angles measures 82o and 72o respectively.

NCERT Solutions for Class 7 Maths Chapter 5Lines and Angles Line l is not parallel to line m.

If two adjacent angles are supplementary, they form a linear pair. (v) If two lines intersect at a point, then the vertically opposite angles are always _. Solution:- If two lines intersect at a point, then the vertically opposite angles are always equal. (vi) If two lines intersect at a point, and if one pair of vertically opposite angles .

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