Question

In ∆PQR, measure of ∠P=800

and ∠Q=650
Find the measure of the exterior angle at
vertex R​

Answer 1

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By using the theorem,If two sides of a triangle are equal then the opposite angles to the sides are equal.

⇒ If PQ=PR then ∠Q=∠R

In △PQR,

⇒∠P+∠Q+∠R=180∘

⇒∠P+∠Q+∠R=180∘ since ∠Q=∠R=65∘(given)

⇒∠P+2×65∘=180∘

⇒∠P=180∘−130∘=50∘

∴∠P=50∘

Answer 2

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By using the theorem,If two sides of a triangle are equal then the opposite angles to the sides are equal.

⇒ If PQ=PR then ∠Q=∠R

In △PQR,

⇒∠P+∠Q+∠R=180∘

⇒∠P+∠Q+∠R=180∘ since ∠Q=∠R=65∘(given)

⇒∠P+2×65∘=180∘

⇒∠P=180∘−130∘=50∘

∴∠P=50∘