Question

Solve for X then find the measure of DEF. Write your answers in decimal form.

Answer 1

Since EF bisects ∠DEF, we know that EF splits ∠DEF in 2 halves from the word 'bisects', which can be written as 'bi- sects' , where bi means 2 and sects means sections

Hence, ∠DEG = ∠GEF --------------(1)

We are given the measure of these angles:

∠DEG = 3x - 4

∠GEF = x + 13

Now, replacing the values in (1):

3x - 4 = x + 13

2x = 17

x = 17/2

Now, finding the measure of ∠DEF:

∠DEF = ∠DEG + ∠GEF

∠DEF = 3x - 4 + x + 13

∠DEF = (51 / 2) - 4 + (17/2) + 13 (x = 17/2)

∠DEF = 34 - 4 + 13

∠DEF = 43°