In ΔRST, m ∠ R = ( 11 x + 3 ) ∘ m∠R=(11x+3) ∘ , m ∠ S = ( x + 15 ) ∘ m∠S=(x+15) ∘ , and m ∠ T = ( 2 x + 8 ) ∘ m∠T=(2x+8) ∘ . Find m ∠ R . m∠R.

Question

In ΔRST, m∠R=(11x+3)∘m∠R=(11x+3)∘, m∠S=(x+15)∘m∠S=(x+15)∘, and m∠T=(2x+8)∘m∠T=(2x+8)∘. Find m∠R.m∠R.

Answer 1

Hi Samera M

The angles in a triangle sum to 180°

So

11x + 3 + x + 15 + 2x + 8 = 180

Solve this for x

Plug x into the equations given for ∠mR

Answer 2

Consider the important fact given in the question: ΔRST is a triangle.

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

m∠R + m∠S + m∠T= 180 °

(11x+3) + (x+15) + (2x+8) = 180

To find m∠R, we must first determine the value of x.

14x + 26 = 180

14x = 154

x = 11

Now, we may find m∠R as (11x+3).

m∠R = 11*11 + 3

m∠R = 124°

To check:

m∠S=(x+15) = 26°

m∠T=(2x+8) = 22+8 = 30°

Does 124+26+30 = 180 ?

180 = 180 ? YES