To find the measure of ∠F, we need to find the value of x. Since ∠D and ∠E are supplementary angles, their measures should add up to 180°.
So we can write the equation: (4x+8)° + (x+17)° = 180°
Combining like terms, we get: 5x + 25 = 180
Subtracting 25 from both sides, we get: 5x = 155
Dividing both sides by 5, we get: x = 31
Now we can find the measure of ∠F by substituting the value of x back into the equation of ∠D.
∠D = (4x+8)°
∠D = (4(31)+8)°
∠D = 124°
Since ∠F is a vertical angle with ∠D, ∠F will also have a measure of 124°.
Therefore, the measure of ∠F is 124°.
Answer: 124°
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?
132°
124°
31°
48°
1 answer