Question

If there are two supplementary angles, <D and LE, where m/D = (4x + 8) ° and mLE = (x + 17) °

, and LF is a vertical angle with LD, what is the measure of LF?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since LF is a vertical angle with LD, the measure of LF is equal to the measure of LD.

Given that mD = (4x + 8)° and mLE = (x + 17)° and they are supplementary angles, we can set up the equation:

mD + mL E = 180°

(4x + 8) + (x + 17) = 180

5x + 25 = 180

5x = 155

x = 31

Substituting the value of x back into the expressions for mD and mL E:

mD = (4x + 8)° = (4(31) + 8)° = 132°

mLE = (x+ 17)° = (31 + 17)° = 48°

Since LF is a vertical angle with LD, the measure of LF is equal to the measure of LD, which is 132°.