Answer:
[tex]\angle ACD=124\°\\\\\angle CED=64\°[/tex]
Step-by-step explanation:
To solve this exercise you need to remember:
1. The sum of the Interior angles of a triangle is 180 degrees.
2. Straight angles are those angles that measure 180 degrees.
3. Supplementary angles are those angles whose sum is 180 degrees.
4. Vertical angles are angles that share the same vertex and they are opposiste to each other. They are congruent.
Knowing the above, you can set up the following equation:
[tex]31\°+93\°+\angle ACB=180\°[/tex]
Solving the equation, you get:
[tex]\angle ACB=180\°-124\°=56\°[/tex]
Since [tex]\angle ACB[/tex] and [tex]\angle DCE[/tex] are Vertical angles:
[tex]\angle ACB=\angle DCE=56\°[/tex]
Knowing the measure of [tex]\angle DCE[/tex] , you can write the following equation to find [tex]\angle CED[/tex]:
[tex]56\°+60\°+\angle CED=180\°[/tex]
Solve the equation:
[tex]\angle CED=180\°-116\°=64\°[/tex]
As you can observe in the figure, the angles [tex]\angle DCE[/tex] and [tex]\angle ACD[/tex] are Supplementary. Then:
[tex]\angle ACD+\angle DCE=180\°\\\\\angle ACD+56\°=180\°[/tex]
Solving for [tex]\angle ACD[/tex], you get:
[tex]\angle ACD=180\°-56\°=124\°[/tex]
