Question

in the given figure measure of angle QPR is.....​

Answer 1

Answer:

Angle QPR = 2 (QTR)

= 2 ( 21 )

= 42.

Please mark it as brainliest.

Answer 2

Given:

Δ PQR and ΔTQR

∠PQR = 2x

∠PRS= 2y

∠QTY= 21°

To find:

∠QPR

Solution:

In Δ TQR,

∠TRS 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 ∠PRS = 1/2 ∠PQR+21°     - (1)

Now in ΔPQR,

∠PRS is the exterior angle

Again using the exterior angle theorem we get:

∠PRS = ∠PQR + ∠QPR         - (2)

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

1/2 (∠QPR + ∠PQR) = 1/2 ∠PQR + ∠QTR

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°.