Question

If there are two supplementary angles, LD and LE,

where mLD = (4x + 8) * and mLE = (I + 17) *, and LF
a vertical angle with LD, what is the measure of LF?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the measure of LF, we need to find the measure of LD and LE first.

Given: mLD = (4x + 8)* and mLE = (I + 17)*

Since LD and LE are supplementary angles, their measures add up to 180 degrees: mLD + mLE = 180.

Substitute the given measures: (4x + 8) + (I + 17) = 180.

Combine like terms: 4x + 8 + I + 17 = 180.

Combine like terms again: 4x + I + 25 = 180.

Subtract 25 from both sides: 4x + I = 155. (equation 1)

Since LF is a vertical angle with LD, their measures are equal: mLF = mLD.

Substitute the measure of LD: mLF = (4x + 8)*.

So, the measure of LF is (4x + 8)*.