Answer:
[tex]m\angle CED= 64\°[/tex]
[tex]m\angle ACD=124\°[/tex]
Step-by-step explanation:
In the figure given:
∠ABC = 93°
∠BAC = 31°
∠CDE = 60°
To find ∠CED and ∠ACD.
Solution:
In triangle ABC, we are given two vertex angles. We can find the third angle as angle sum of triangle = 180°.
∠ABC = 93° , ∠BAC = 31°
∠BCA= [tex]180\°-(93\°+31\°)[/tex]
∠BCA = 56°
[tex]m\angle BCA+m\angle ACD=180\°[/tex] [Supplementary angles forming a linear pair]
[tex]m\angle ACD=180\°-56\°[/tex]
[tex]m\angle ACD=124\°[/tex] (Answer)
In triangle CDE:
[tex]m\angle CDE+m\angle CED = m\angle ACD[/tex] [Exterior angle theorem :Exterior angle of a triangle is equal to sum of opposite interior angles ]
[tex]60\°+m\angle CED = 124\°[/tex]
[tex]m\angle CED= 124\°-60\°[/tex]
[tex]m\angle CED= 64\°[/tex] (Answer)
