A day full of math games & activities. Find one near you.

In Fig. 5.32, if PQ||RS and QR||TS, then the value a is
a. 95°
b. 90°
c. 85°
d. 75°

In Fig. 5.32, if PQ||RS and QR||TS, then the value a is: a. 95°, b. 90°, c. 85°, d. 75°

Solution:

Given, PQ||RS and QR||TS

We have to find the value of a.

Considering PQ || RS intersected by a transversal QR,

If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.

∠PQR = ∠SRQ

From the figure,

∠PQR = 85°

So, ∠SRQ = 85°

Considering QR || TS intersected by a transversal RS,

If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.

∠SRQ = ∠RST

So, ∠RST = 85°

We know that the sum of a linear pair of angles is always equal to 180 degrees.

∠RST+ a = 180°

85° + a = 180°

a = 180° - 85°

Therefore, a = 95°

✦ Try This: In the figure, given that ∠1 = ∠2 and ∠3 ≡ ∠4 Prove that ∆MUG ≡ ∆ TUB.

In the figure, given that ∠1 = ∠2 and ∠3 ≡ ∠4 Prove that ∆MUG ≡ ∆ TUB

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

NCERT Exemplar Class 7 Maths Chapter 5 Problem 41

In Fig. 5.32, if PQ||RS and QR||TS, then the value a is: a. 95°, b. 90°, c. 85°, d. 75°

Summary:

In Fig. 5.32, if PQ||RS and QR||TS, then the value a is 95°

☛ Related Questions: