Answer:
Part 1) m∠1=45°
Part 2) m∠3=45°
Part 3) m∠2=135°
Part 4) m∠4=135°
Step-by-step 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°
