Question

Solve for x using the given information.GIVEN: ∠D is congruent to ∠DEG, Ray EG bisects ∠DEF.

Answer 1

x = 15 degrees

Step-by-step explanation:

First, ∠D is congruent to ∠DEG

`\angle D\cong\angle E`

Since EG bisects ∠DEF

`\angle\text{DEG}\cong\angle\text{GEF}`

Therefore:

`\begin{gathered} \angle D\cong\angle\text{DEG}\cong\angle\text{GEF} \\ 4x=2x+30 \\ 4x-2x=30 \\ 2x=30 \\ x=(30)/(2) \\ x=15^0 \end{gathered}`

The value of x is 15.