Question

find angle R
I will make him brainlist and give step by step answer​

Answer 1

⇒ Given:

A triangle with 2 interior angles and one exterior angle marked.

⇒ To Find:

The measure of ∠PRQ.

⇒ What are the concepts used?

The main concepts to be kept in mind while solving this question must be the angle sum property of a triangle and the the straight angle formation property in triangles. Both of them are explained below:

• According to the angle sum property of a triangle, the sum of all the three interior angles of a triangle is always equal to 180°.

• As per the straight angle formation property, if any side of a triangle is extended outwards, then the sum of the interior angle and the exterior angle on the side would always be equal to 180°.

⇒ Solution:

∠PQS = 130°

As ∠PQS and ∠PQR form a straight ray SR, the sum of both the angles is 180°.

Forming a statement:

∠PQS + ∠PQR = 180°

∠PQS = 130°

130° + ∠PQR = 180°

So, ∠PQR = 180° - 130°

∠PQR = 50°

We know that the sum of all the three angles of a triangle is 180°.

That is, the sum of angles PRQ, PQR and QPR is 180°.

Forming a statement:

∠PRQ + ∠PQR + ∠QPR = 180°

Substituting the values in the equation:

= (4x + 15)° + 50° + (5x - 2)° = 180°

= 4x + 15 + 50 + 5x - 2= 180°

= 9x + 63 = 180°

= 9x = 180 - 63

= 9x = 117

Therefore:

$\sf{x=\dfrac{117}{9}}$

$\sf{x=13}$

Here, we are asked to find the value of ∠PRQ.

Value of angle PRQ = 4x + 15°

We know that x is 13.

So,

∠PRQ = (4 x 13) + 15

∠PRQ = 52 + 15

∠PRQ = 67°

Therefore, the value of angle R is 67°.