Question

Bonus: In Triangle STP, the measure of <T is twice the measure of <S and the

measure of <P is three times the measure of <S. What is the measure of all three angles?

ENTER ONLY NUMBERS IN THE BOXES:
m<S = degrees

m<T= degrees

m<P= degrees
​

Answer 1

m∠S=30°

m∠T=60°

m∠P=90°

Explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

In the triangle STP

m∠S+m∠T+m∠P=180° ----> equation A

m∠T=2(m∠S) ----> equation B

m∠P=3(m∠S) ----> equation C

Solve the system of equations by substitution

Substitute equation B and equation C in equation A

m∠S+2(m∠S)+3(m∠S)=180°

Solve for m∠S

6m∠S=180°

m∠S=30°

Find m∠T

m∠T=2(m∠S)

m∠T=2(30°)=60°

Find m∠P

m∠P=3(m∠S)

m∠P=3(30°)=90°