In Fig. 5.23, if QP || SR, the value of a is
a. 40°
b. 30°
c. 90°
d. 80°

Solution:

Given, QP || SR

We have to find the value of a.

Draw a line LM such that LM ∣∣ PQ ∣∣ SR

Now, LM is parallel to QP cut by transversal QT.

We know that the alternate interior angles are equal.

So, ∠LTQ = ∠PQT

From the figure,

∠PQT = 60°

So, ∠LTQ=60° --------------------(1)

Similarly, LM is parallel to SR cut by a transversal TS..

So, ∠TSR = ∠LTS

From the figure,

∠TSR = 30°

So, ∠LTS = 30° --------------------- (2)

From equation 1 and 2,

a = ∠LTQ + ∠LTS

= 60° + 30°

= 90°

Therefore, the value of a is 90 degrees.

✦ Try This: In the given figure, write down each pair of vertically opposite angles.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

---

NCERT Exemplar Class 7 Maths Chapter 5 Problem 27

In Fig. 5.23, if QP || SR, the value of a is: a. 40°, b. 30°, c. 90°, d. 80°

Summary:

In Fig. 5.23, if QP || SR, the value of a is 90°

---

☛ Related Questions:

• In which of the following figures, a and b are forming a pair of adjacent angles
• In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) . . . .
• In Fig. 5.25, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to, a . . . .