f there are two supplementary angles, ∠D and ∠E , where m∠D=(4x+8)° and m∠E=(x+17)° , and ∠F is a vertical angle with ∠D , what is the measure of ∠F ? (1 point) Responses 132° 132 degrees 48° 48 degrees 124° 124 degrees 31° 31 degrees

Answer 1

The measure of ∠D is (4x+8)° and the measure of ∠E is (x+17)°. Since ∠D and ∠E are supplementary angles, we know that their sum is 180°.

(4x+8)° + (x+17)° = 180°

Combining like terms, we get:

5x + 25 = 180

Subtracting 25 from both sides:

5x = 155

Dividing both sides by 5:

x = 31

Now that we know x is 31, we can find the measure of ∠D:

∠D = 4x + 8 = 4(31) + 8 = 124°

Since ∠F is a vertical angle with ∠D, ∠F must have the same measure as ∠D. Therefore, the measure of ∠F is 124°.

So, the correct answer is 124°.