find angle R
I will make him brainlist and give step by step answer
Answers
⇒ 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:
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°