Question

In the given figure , measure of angle QPR is
a. 10.5°
b. 42°
c. 111°
d. 50°

Answer 1

42 is the correct answer

Answer 2

Given:

Δ PQR and ΔSQR

∠PQR = 2x

∠PRT= 2y

∠QSR= 21°

To find:

∠QPR

Solution:

In Δ SQR,

∠SRT is an exterior angle = y

Since the exterior angle of a triangle equals the sum of interior opposite angles,

⇒ y = x + 21°

or 1/2 ∠PRT = 1/2 ∠PQR+21°     - (1)

Now in ΔPQR,

∠PRT is the exterior angle

Again using the exterior angle theorem we get:

∠PRT = ∠PQR + ∠QPR         - (2)

Substituting value of ∠PRT from (2) in (1)

1/2 (∠QPR + ∠PQR) = 1/2 ∠PQR + ∠QSR

Opening the brackets and solving, we get:

1/2 ∠PQR + 1/2 ∠QPR  - 1/2 ∠PQR = 21°

or 1/2 ∠QPR = 21°

or ∠QPR = 42°

Hence, angle QPR IS 42°.