Answer:
The measure of the angles are
m∠1=128°
m∠2=52°
m∠3=52°
m∠4=128°
m∠5=128°
m∠6=128°
m∠7=52°
m∠8=52°
Step-by-step explanation:
see the attached figure with numbers to better understand the problem
step 1
Find the measure of angle 5
we know that
m∠5+52°=180° ----> by consecutive interior angles
m∠5=180°-52°=128°
step 2
Find the measure of angle 8
we know that
m∠8=52° ----> by vertical angles
step 3
Find the measure of angle 7
we know that
m∠7=m∠8 ----> by corresponding angles
we have
m∠8=52°
therefore
m∠7=52°
step 4
Find the measure of angle 6
we know that
m∠6+m∠7=180° ----> by supplementary angles
we have
m∠7=52°
therefore
m∠6+52°=180°
m∠6=180°-52°=128°
step 5
Find the measure of angle 3
we know that
m∠3+m∠6=180° ----> by consecutive interior angles
we have
m∠6=128°
m∠3=180°-128°=52°
step 6
Find the measure of angle 2
we know that
m∠2=m∠3 ----> by vertical angles
we have
m∠3=52°
therefore
m∠2=52°
step 7
Find the measure of angle 1
we know that
m∠1+m∠3=180° ----> by supplementary angles
we have
m∠3=52°
therefore
m∠1+52°=180°
m∠1=180°-52°=128°
step 8
Find the measure of angle 4
we know that
m∠4=m∠1 ----> by vertical angles
we have
m∠1=128°
therefore
m∠4=128°
