Question

In A/EFG, MZE = (8x – 16)", mZF = (x + 8)°, and m2 = (2x – 10°.)mZGWhat is the value of x?

Answer 1

x = 18

Explanation:

m∠E = (8x – 16)°

m∠F = (x + 8)°

m∠G = (2x - 10)°

The three angles make up triangle EFG

m∠E + m∠F + m∠G = 180° (sum of angles in a triangle)

8x -16 + x + 8 + 2x - 10 = 180

collect like terms:

8x + x + 2x -16 + 8 - 10 = 180

11x - 18 = 180

add 18 to both sides:

11x - 18 + 18 = 180 + 18

11x = 198

divide both sides by 11:

$\begin{gathered} \frac{11x}{11}\text{ = }\frac{198}{11} \\ x\text{ = }18 \end{gathered}$