Question

Two triangles, equilateral triangle PQS and isosceles triangle PQR given that PRQ=86

Answer 1

Explanation:

As Given, ∠PQR=∠PRQ

To prove: ∠PQS=∠PRT

According to the question,

∠PQR+∠PQS=180

∘

∣ Linear Pair

⇒∠PQS=180

∘

−∠PQR--- (i)

Also ∠PRQ+∠PRT=180

∘

∣ Linear Pair

⇒PRT=180

∘

−∠PRQ

⇒∠PRQ=180

∘

−∠PQR−−−(ii)(∠PQR=∠PRQ)

From (i) and (ii),

∠PQS=∠PRT=180

∘

−∠PQR

∴∠PQS=∠PRT [henceproved