Question

In figure, PQ = PR, RS = RQ and ST || QR. if the exterior angle RPU is 140°, then find the measure of ∠TSR.
Pls tell I am so confused...

Answer 1

☞︎︎︎ Solution :

$\:$

★ Consider the ΔPQR :

$\:$

• From Exterior Angle Property -

$\:$

⇒ ∠RPU - ∠PRQ + ∠PQR

$\:$

• Transposing The Terms

$\:$

⇒ ∠RPU = ∠PRQ + ∠PQR

$\:$

⇒ 140° = 2∠PQR (PQ = PR)

$\:$

$\large \rm⇒ \: \angle PQR \: = \dfrac{140 \degree}{2}$

$\:$

⇒ ∠PQR = 70°

$\:$

★ Given :

$\:$

• ST || QR

• QR is Transversal

$\:$

☞︎︎︎ Corresponding angles Property -

$\:$

⇒ ∠PST =∠PQR = 70°

$\:$

★ Consider triangle QSR :

$\:$

• RS = RQ (from question)

$\:$

So,

$\:$

⇒ ∠SQR - ∠RSQ = 70°

$\:$

• PQ is a straight line -

$\:$

⇒ ∠PST + ∠TSR + ∠RSQ = 180°

$\:$

⇒ 70° + ∠TSR + 70° = 180°

$\:$

⇒ 140° + ∠TSR = 180°

$\:$

⇒ ∠TSR = 180° – 140°

$\:$

∴ ∠TSR = 40

Answer 2

Answer:

hope

it

help

you

please

mark

me

as

brain

list