Question

If the measure of angle BEF is 2x + 10, and the measure of angle DFE is 4x - 8, determine the value of x. Then, find the measures of angle BEF and angle DFE.

A. x=9x=9, BEF = 28°, DFE = 28°
B. x=5x=5, BEF = 20°, DFE = 12°
C. x=18x=18, BEF = 36°, DFE = 64°
D. x=14x=14, BEF = 38°, DFE = 52°

Answer 1

To find the value of x, set the measure of angle BEF equal to the measure of angle DFE and solve for x. When x = 9, the measures of angles BEF and DFE are both 28°. Hence the correct answer is option A

Step-by-step explanation:

To find the value of x, we set the measure of angle BEF equal to the measure of angle DFE: 2x + 10 = 4x - 8. We can solve for x by subtracting 2x and adding 8 to both sides of the equation: 10 + 8 = 4x - 2x. Combine like terms to get 18 = 2x. Divide both sides by 2 to isolate x: x = 9.

Now that we know x = 9, plug this value back into the expressions for the measures of angles BEF and DFE. BEF = 2(9) + 10 = 28° and DFE = 4(9) - 8 = 28°.

Hence the correct answer is option A