Question

What is the measure of angle R?

Answer 1

m∠ R = 52.5°

Explanation:

There are two approaches to this problem;

1. Apply the Sum of Angles in Triangle Theorem to be ⇒ 180°,

2. By Base Angles Theorem concluding that this is an isosceles triangle, the base angles are ≅

For the simplicity let us consider the second option;

m∠ R = m∠ T, m∠ R = 3x + 20

However, we need to apply the first approach to this second part of the problem as to derive the value of x, and thus the measure of ∠ R;

m∠ S + m∠ T + m∠ R = 180,

12x - 15 + 3x + 30 + 3x + 30 = 180,

18x + 45 = 180,

18x = 135,

x = 7.5

Thus the measure of ∠ R ⇒ 3 ( 7.5 ) + 30 = 22.5 + 30 ⇒ 52.5 degrees

* Answer: m∠ R = 52.5° *

Answer 2

52.5

Explanation:

Since this is an isosceles triangle, the base angles are the same

The three angles add to 180

R+ T + S = 180

3x+30 + 3x+30 + 12x-15 = 180

Combine like terms

18x +45 = 180

Subtract 45 from each side

18x+45 - 45 = 180-45

18x =135

Divide each side by 18

18x/18 = 135/18

x = 7.5

We want angle R

R = 3x+30

= 3( 7.5) +30

22.5 +30

52.5