NCERT Exemplar Solutions
Class 7 - Mathematics

Unit 5: Lines And Angles

If sum of measures of two angles is 90°, then the angles are ______.

If the sum of measures of two angles is 180°, then they are ______.

A transversal intersects two or more than two lines at ______ points.

Sum of interior angles on the same side of a transversal is ______.

Alternate interior angles have one common ______.

Corresponding angles are on the ______ side of the transversal.

Alternate interior angles are on the ______ side of the transversal.

Two lines in a plane which do not meet at a point anywhere are called ______ lines.

Two angles forming a ______ pair are supplementary.

The supplement of an acute is always ______ angle.

The supplement of a right angle is always ______ angle.

The supplement of an obtuse angle is always ______ angle.

In a pair of complementary angles, each angle cannot be more than ______.

An angle is 45°. Its complementary angle will be ______.

An angle which is half of its supplement is of ______.

Two right angles are complementary to each other.

One obtuse angle and one acute angle can make a pair of complementary angles.

Two supplementary angles are always obtuse angles.

Two right angles are always supplementary to each other.

One obtuse angle and one acute angle can make a pair of supplementary angles.

Both angles of a pair of supplementary angles can never be acute angles.

Two supplementary angles always form a linear pair.

Two angles making a linear pair are always supplementary.

Two angles making a linear pair are always adjacent angles.

Vertically opposite angles form a linear pair.

Interior angles on the same side of a transversal with two distinct parallel lines are complementary angles.

Vertically opposite angles are either both acute angles or both obtuse angles.

A linear pair may have two acute angles.

An angle is more than 45°. Its complementary angle must be less than 45°.

Two adjacent angles always form a linear pair.

72. Write down each pair of adjacent angles shown in the following figures:

73. In each of the following figures, write, if any, (i) each pair of vertically opposite angles, and (ii) each linear pair.

74. Name the pairs of supplementary angles in the following figures:

75. In Fig. 5.36, PQ ∥ RS, TR ∥ QU and ∠PTR = 42°. Find ∠QUR.

76. The drawings below (Fig. 5.37) show angles formed by the goalposts at different positions of a football player. The greater the angle, the better the chance the player has of scoring a goal.

(a) Seven football players are practicing their kicks. They are lined up in a straight line in front of the goalpost [Fig. (ii)]. Which player has the greatest kicking angle?

(b) Now the players are lined up as shown in Fig. (iii). Which player has the best kicking angle?

(c) Estimate at least two situations such that the angles formed by different positions of two players are complement to each other.

The sum of two vertically opposite angles is 166°. Find each of the angles.

78. In Fig. 5.38, l ∥ m ∥ n. ∠QPS = 35° and ∠QRT = 55°. Find ∠PQR.

79. In Fig. 5.39, P, Q and R are collinear points and TQ ⟂ PR. Name:

(a) pair of complementary angles

(b) two pairs of supplementary angles

(c) four pairs of adjacent angles

80. In Fig. 5.40, OR ⟂ OP.

(i) Name all the pairs of adjacent angles.

(ii) Name all the pairs of complementary angles.

81. If two angles have a common vertex and their arms form opposite rays (Fig. 5.41), then:

(a) How many angles are formed?

(b) How many types of angles are formed?

(c) Write all the pairs of vertically opposite angles.

82. In Fig. 5.42 are the following pairs of angles adjacent? Justify your answer.

83. In Fig. 5.43, write all the pairs of supplementary angles.

84. What is the type of other angle of a linear pair if

(a) one of its angles is acute?

(b) one of its angles is obtuse?

(c) one of its angles is right?

Can two acute angles form a pair of supplementary angles? Give reason in support of your answer.

86. Two lines AB and CD intersect at O (Fig. 5.44). Write all the pairs of adjacent angles by taking angles 1, 2, 3 and 4 only.

If the complement of an angle is 62°, then find its supplement.

88. A road crosses a railway line at an angle of 30° as shown in Fig. 5.45. Find the values of a, b and c.

89. The legs of a stool make an angle of 35° with the floor as shown in Fig. 5.46. Find the angles x and y.

90. Iron rods a, b, c, d, e and f are making a design in a bridge as shown in Fig. 5.47, in which a ∥ b, c ∥ d, e ∥ f. Find the marked angles between

(i) b and c

(ii) d and e

(iii) d and f

(iv) c and f

91. Amisha makes a star with the help of line segments a, b, c, d, e and f, in which a ∥ d, b ∥ e and c ∥ f. Chhaya marks an angle as 120° as shown in Fig. 5.48 and asks Amisha to find the ∠x, ∠y and ∠z. Help Amisha in finding the angles.

92. In Fig. 5.49, AB ∥ CD, AF ∥ ED, ∠AFC = 68° and ∠FED = 42°. Find ∠EFD.

93. In Fig. 5.50, OB is perpendicular to OA and ∠BOC = 49°. Find ∠AOD.

94. Three lines AB, CD and EF intersect each other at O. If ∠AOE = 30° and ∠DOB = 40° (Fig. 5.51), find ∠COF.

Measures (in degrees) of two complementary angles are two consecutive even integers. Find the angles.

If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is 20°, find the angles.

Two angles are making a linear pair. If one of them is one-third of the other, find the angles.

Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

99. In Fig. 5.52, AE ∥ GF ∥ BD, AB ∥ CG ∥ DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.

100. In Fig. 5.53, find the value of ∠BOC, if points A, O and B are collinear.

101. In Fig. 5.54, if l ∥ m, find the values of a and b.

102. In Fig. 5.55, l ∥ m and a line t intersects these lines at P and Q, respectively. Find the sum 2a + b.

103. In Fig. 5.56, QP ∥ RS. Find the values of a and b.

104. In Fig. 5.57, PQ ∥ RT. Find the value of a + b.

105. In Fig. 5.58, PQ, RS and UT are parallel lines.

(i) If c = 57° and a = c/3, find the value of d.

(ii) If c = 75° and a = (2/5)c, find b.

106. In Fig. 5.59, AB ∥ CD. Find the reflex ∠EFG.

107. In Fig. 5.60, two parallel lines l and m are cut by two transversals n and p. Find the values of x and y.

108. In Fig. 5.61, l, m and n are parallel lines, and the lines p and q are also parallel. Find the values of a, b and c.

109. In Fig. 5.62, state which pair of lines are parallel. Give reason.

110. In Fig. 5.63, examine whether the following pairs of lines are parallel or not:

(i) EF and GH

(ii) AB and CD

111. In Fig. 5.64, find out which pair of lines are parallel:

112. In Fig. 5.65, show that:

(i) AB ∥ CD

(ii) EF ∥ GH

113. In Fig. 5.66, two parallel lines l and m are cut by two transversals p and q. Determine the values of x and y.