Question

In triangle PQR,angle RQP = 35 and PQ = PR.What will be the value of angle QPR?

85
90
105
110
no explanation​

Answer 1

Answer:

Given, in △PQR,PQ=PR

Therefore, △PQR is an isosceles triangle with equal base

RQP = 35°

PRQ = 35° ( Because it is an isosceles triangle)

RPQ + RQP + PRQ = 180° ( Sum of interior angles)

RPQ + 35° + 35° = 180°

RPQ + 70° = 180°

RPQ = 180° - 70°

RPQ = 110°

Answer 2

Solution :-

from image, in ∆PQR we have,

→ ∠PQR = 35°

→ PQ = PR .

So,

→ ∠PRQ = ∠PQR { Angle opposite to equal sides are equal in measure . }

→ ∠PRQ = 35° .

now,

→ ∠PRQ + ∠PQR + ∠QPR = 180° { By angle sum property. }

→ 35° + 35° + ∠QPR = 180°

→ 70° + ∠QPR = 180°

→ ∠QPR = 180° - 70°

→ ∠QPR = 110° (Ans.)

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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