Answer:
Part a) [tex]m<CED=64\°[/tex]
Part b) [tex]m<ACD=124\°[/tex]
Step-by-step explanation:
step 1
Find the measure of angle ACB
we know that
The sum of the measures of interior angle of a triangle must be equal to [tex]180\°[/tex]
so
In the triangle ABC
[tex]m<ACB+93\°+31\°=180\°[/tex]
[tex]m<ACB+124\°=180\°[/tex]
[tex]m<ACB=180\°-124\°=56\°[/tex]
step 2
Find the measure of angle ACD
we know that
[tex]m<ACD+m<ACB=180\°[/tex] -------> by supplementary angles
we have
[tex]m<ACB=56\°[/tex]
substitute
[tex]m<ACD+56\°=180\°[/tex]
[tex]m<ACD=180\°-56\°=124\°[/tex]
step 3
Find the measure of angle CED
we know that
m<DCE=m<ACB ------> by vertical angles
so
[tex]m<DCE=56\°[/tex]
Remember that
The sum of the measures of interior angle of a triangle must be equal to [tex]180\°[/tex]
so
In the triangle CDE
[tex]56\°+60\°+m<CED=180\°[/tex]
[tex]116\°+m<CED=180\°[/tex]
[tex]m<CED=180\°-116\°=64\°[/tex]
