To find the measure of angle ∠F, we need to understand that vertical angles are always congruent. Therefore, ∠D = ∠F and we can equate their measures:
m∠D = m∠F
4x + 8 = x + 17
Now, let's solve for x:
3x = 9
x = 3
Substitute the value of x back into the equation for ∠F:
m∠F = 4x + 8 = 4(3) + 8 = 12 + 8 = 20
Therefore, the measure of angle ∠F is 20 degrees.
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
132°
132 degrees
31°
31 degrees
48°
48 degrees
124°
124 degrees
3 answers
thatas not an answer choice
Apologies for the confusion. Since ∠D and ∠E are supplementary angles, we know that their measures add up to 180 degrees:
m∠D + m∠E = 180
Substituting the given measures:
(4x + 8) + (x + 17) = 180
Combining like terms:
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing both sides by 5:
x = 31
Now, we can find the measure of ∠F by substituting the value of x into the measure of ∠D:
m∠F = 4x + 8 = 4(31) + 8 = 124 + 8 = 132
Therefore, the measure of ∠F is 132 degrees. The correct answer choice is:
132°
m∠D + m∠E = 180
Substituting the given measures:
(4x + 8) + (x + 17) = 180
Combining like terms:
5x + 25 = 180
Subtracting 25 from both sides:
5x = 155
Dividing both sides by 5:
x = 31
Now, we can find the measure of ∠F by substituting the value of x into the measure of ∠D:
m∠F = 4x + 8 = 4(31) + 8 = 124 + 8 = 132
Therefore, the measure of ∠F is 132 degrees. The correct answer choice is:
132°