Question

In ΔCDE, \overline{CE}

Answer 1

Answer:

$m\angle CDE=14^o$

Step-by-step explanation:

we know that

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

see the attached figure to better understand the problem

so

∠DEF=∠ECD+∠CDE

substitute the given values

$(4x+5)^o=(x+9)^o+(x+8)^o$

solve for x

Combine like terms

$(4x+5)^o=(2x+17)^o$

Group terms

$4x-2x=17-5$

$2x=12$

$x=6$

Find the measure of angle CDE

$m\angle CDE=(x+8)^o$

substitute the value of x

$m\angle CDE=(6+8)=14^o$