Question

Find the measures of:

all angles if 3(m∠1+m∠3) = m∠2+m∠4

Answer 1

Part 1) m∠1=45°

Part 2) m∠3=45°

Part 3) m∠2=135°

Part 4) m∠4=135°

Explanation:

we know that

m∠1=m∠3 -----> by vertical angles Equation A

m∠2=m∠4 -----> by vertical angles Equation B

m∠1+m∠2=180° ----> by supplementary angles (linear pair) Equation C

3(m∠1+m∠3) = m∠2+m∠4 ----> Equation D

Substitute equation A and equation B in equation D

3(m∠1+m∠1) = m∠2+m∠2

6(m∠1) = 2m∠2

3(m∠1) =m∠2 -----> equation E

Substitute equation E in equation C and solve for m∠1

m∠1+3(m∠1)=180°

4(m∠1)=180°

m∠1=45°

Find the measure of m∠3

Remember that

m∠1=m∠3 (equation A)

therefore

m∠3=45°

Find the measure of m∠2

Remember that

m∠2=3(m∠1) (equation E)

substitute the value of m∠1

m∠2=3(45°)=135°

Find the measure of m∠4

Remember that

m∠2=m∠4 (equation B)

therefore

m∠4=135°