Question

Question

If 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

124°
124 degrees

31°
31 degrees

132°
132 degrees

48°

Answer 1

Supplementary angles add up to 180°. Therefore, we can set up the equation:

\[ m∠D + m∠E = 180° \]

Substituting the expressions for the angles:

\[ (4x + 8) + (x + 17) = 180 \]

Combining like terms:

\[ 5x + 25 = 180 \]

Next, we can isolate \(x\) by subtracting 25 from both sides:

\[ 5x = 155 \]

Now, divide by 5:

\[ x = 31 \]

Now we can find the measure of ∠D:

\[ m∠D = 4x + 8 = 4(31) + 8 = 124 + 8 = 132° \]

Since ∠F is a vertical angle with ∠D, they are equal in measure. Thus:

\[ m∠F = m∠D = 132° \]

The final answer is:

132°