Answer:
Part 9)
m∠1=88°
m∠2=33°
m∠3=88°
m∠4=59°
Part 10)
m∠1=47°
m∠2=43°
m∠3=90°
m∠4=43°
Step-by-step explanation:
Part 9)
Find the measure of m∠1
we know that
33°+m∠1+59°=180° ----> by a straight angle
so
m∠1+92°=180°
m∠1=180°-92°
m∠1=88°
Find the measure of m∠2
we know that
m∠2=33° ----> by vertical angles
Find the measure of m∠3
we know that
m∠2=m∠1 ----> by vertical angles
we have
m∠1=88°
so
m∠3=88°
Find the measure of m∠4
we know that
m∠4=59° ----> by vertical angles
Part 10)
Find the measure of m∠1
we know that
m∠1=47° ----> by vertical angles
Find the measure of m∠2
we know that
m∠1+m∠2=90° ----> by complementary angles
we have
m∠1=47°
substitute
47°+m∠2=90°
m∠2=90°-47°
m∠2=43°
Find the measure of m∠3
we know that
m∠3=90° ----> by vertical angles
Find the measure of m∠4
we know that
m∠4=m∠2 ----> by vertical angles
we have
m∠2=43°
so
m∠4=43°
