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 ?
Since ∠D and ∠E are supplementary angles, their sum is 180°. We can set up the equation as follows:
(4x + 8) + (x + 17) = 180
Simplifying the equation, we combine like terms:
5x + 25 = 180
To isolate x, we subtract 25 from both sides:
5x = 155
Next, we solve for x by dividing both sides by 5:
x = 31
Now that we have the value of x, we can substitute it back into the equation to find the measure of ∠D:
m∠D = (4x + 8)°
m∠D = (4(31) + 8)°
m∠D = (124 + 8)°
m∠D = 132°
Now that we know the measure of ∠D, we can conclude that ∠F, being a vertical angle with ∠D, must have the same measure. Therefore, the measure of ∠F is also 132°.