Question

What is the measure of {CED and {ACD?

Answer 1

Part a)
`m<CED=64\°`

Part b)
`m<ACD=124\°`

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
`180\°`

so

In the triangle ABC

`m<ACB+93\°+31\°=180\°`

`m<ACB+124\°=180\°`

`m<ACB=180\°-124\°=56\°`

step 2

Find the measure of angle ACD

we know that

`m<ACD+m<ACB=180\°` -------> by supplementary angles

we have

`m<ACB=56\°`

substitute

`m<ACD+56\°=180\°`

`m<ACD=180\°-56\°=124\°`

step 3

Find the measure of angle CED

we know that

m<DCE=m<ACB ------> by vertical angles

so

`m<DCE=56\°`

Remember that

The sum of the measures of interior angle of a triangle must be equal to
`180\°`

so

In the triangle CDE

`56\°+60\°+m<CED=180\°`

`116\°+m<CED=180\°`

`m<CED=180\°-116\°=64\°`