Answer:
m∠ R = 52.5°
Step-by-step 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° *
