If there r 2 supplementary angles, <D and <E, where m<D = ( 4x + 8) and m<E = ( x + 17 ) and <F is a vertical angle with <D, wut is the measure of <F?

Question

132

48

31

124

Answer 1

Supplementary angles add up to 180 degrees. Given that <D and <E are supplementary angles, we can set up the equation:

\[ m<D + m<E = 180 \]

Substituting the expressions for the angles, we have:

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

Now, combine like terms:

\[ 4x + x + 8 + 17 = 180 \] \[ 5x + 25 = 180 \]

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

\[ 5x = 155 \]

Now, divide by 5:

\[ x = 31 \]

Now, we can find the measure of angle <D:

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

Since <F is a vertical angle to <D, the measure of <F is equal to the measure of <D.

Therefore,

\[ m<F = 132 \]

Thus, the measure of <F is 132 degrees.