Question

In triangle PQR, side QR is produced to S such that angle PRS= 110⁰, if angle P = angle Q, then angle Q is equal to: A)70⁰.B)55⁰. C)50⁰, D)45⁰.

Answer 1

Answer:

Answer is B=55°

Step-by-step explanation:

Since Q=P

2Q=110

Q=P=55

Answer 2

Step-by-step explanation:

Given: In triangle PQR, side QR is produced to S such that angle PRS= 110⁰, if angle P = angle Q.

To find: Angle Q is equal to:

A)70⁰

B)55⁰

C)50⁰

D)45⁰

Solution:

See the attached figure represents the situation.

As we know that External angle is equal to sum of two opposite internal angles.

As it is given that

$\angle P=\angle Q$

Let say $\angle P=\angle Q=x$

So,

According to the theorem

$x + x = 110$

$2x = 110$

$x = \frac{110}{2}$

$x = 55$

Thus,

$\angle P=\angle Q=55^{\circ}$

Final answer:

$\bf \angle Q=55^{\circ}$

Option B is correct.

Hope it will help you.

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