## ASAPT one year ago Given that D is equidistant to G and F, find m<GED A. 38 degrees B. 40 degrees C. 41 degrees D. 45 degrees

1. ASAPT

@Michele_Laino @ganeshie8

2. Michele_Laino

since the point D is equidistant from G and F, then the line ED is the bisector of the angle GEF, then we can write this: $\Large 2x + 20 = 5x - 10$ please solve for x

3. ASAPT

@Michele_Laino im stuck

4. Michele_Laino

subtractin 2x from both sides, we get: $\Large \begin{gathered} 2x + 20 - 2x = 5x - 10 - 2x \hfill \\ \hfill \\ 20 = 3x - 10 \hfill \\ \end{gathered}$ then adding 10 to both sides we get: $\Large \begin{gathered} 20 + 10 = 3x + 10 - 10 \hfill \\ \hfill \\ 30 = 3x \hfill \\ \end{gathered}$ now divide both sides by 3, what do you get?

5. Michele_Laino

subtracting*

6. ASAPT

so 10?

7. Michele_Laino

ok! we have x=10 so the measure of the angle GED, is: (2*x+20)+(5*x-10)=(2*10+20)+(5*10-10)=...?

8. ASAPT

that's a lot of numbers I don't have much time I have like 17 left and a time limit!!

9. Michele_Laino

hint: $\begin{gathered} \left( {2x + 20} \right) + \left( {5x - 10} \right) = \left( {2 \times 10 + 20} \right) + \left( {5 \times 10 - 10} \right) = ...? \hfill \\ = \left( {20 + 20} \right) + \left( {50 - 10} \right) = 40 + 40 = ...? \hfill \\ \end{gathered}$

10. Michele_Laino

sorry, the angle GEF is 80 degrees, the measure of the angle GED is: $2x + 20 = 2 \times 10 + 20 = ...?$

11. Michele_Laino

$2x + 20 = 2 \times 10 + 20 = 20 + 20 = ...?$