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 ?

Question

31°
31 degrees

48°
48 degrees

132°
132 degrees

124°
124 degrees

Answer 1

To find the measure of ∠F, we need to determine the value of x. Since ∠D and ∠E are supplementary angles, their measures add up to 180°:
(4x + 8)° + (x + 17)° = 180°

Combining like terms:
5x + 25 = 180

Subtracting 25 from both sides of the equation:
5x = 155

Dividing both sides by 5:
x = 31

Now that we know x = 31, we can substitute this value back into the expression for ∠D to find its measure:
m∠D = (4x + 8)°
m∠D = (4(31) + 8)°
m∠D = (124 + 8)°
m∠D = 132°

Since ∠F is a vertical angle with ∠D, it has the same measure:
m∠F = m∠D = 132°

Therefore, the measure of ∠F is 132 degrees.

Answer 2

In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C. If m∠A=x°, m∠B=(2x)°, and m∠C=90°, what is the measure of ∠B?(1 point)
Responses

180 degrees

60 degrees

90 degrees

30 degrees

Answer 3

Since ∠A and ∠B are complementary, their measures add up to 90 degrees. Therefore:

m∠A + m∠B = 90°

Substituting the given values:

x + 2x = 90

Combining like terms:

3x = 90

Dividing both sides by 3:

x = 30

So, the measure of ∠B is 2x = 2(30) = 60 degrees.

Therefore, the measure of ∠B is 60 degrees.