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
31°
31 degrees
48°
48 degrees
132°
132 degrees
124°
To find the measure of ∠F, we can use the fact that vertical angles are congruent.
Since ∠F is a vertical angle with ∠D, they have the same measure.
Therefore, the measure of ∠F is (4x+8)°.
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
31°
31 degrees
48°
48 degrees
132°
132 degrees
124°
To find the measure of ∠F, we can use the fact that vertical angles are congruent.
Since ∠F is a vertical angle with ∠D, they have the same measure.
Therefore, the measure of ∠F is (4x+8)°.
We can substitute the given expressions for the measures of ∠D and ∠E into the equation:
(4x+8)° = (x+17)°
Solving for x:
4x+8 = x+17
3x = 9
x = 3
Now we can find the measure of ∠F:
∠F = (4x+8)°
∠F = (4(3)+8)°
∠F = 20°
Therefore, the measure of ∠F is 20°.