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 ?

Answer 1

If two angles are supplementary, their measures add up to 180 degrees.

Given that m∠D = (4x+8)° and m∠E = (x+17)°, we can set up the equation:

(4x+8)° + (x+17)° = 180°

Combine like terms:

5x + 25 = 180

Subtract 25 from both sides:

5x = 155

Divide both sides by 5:

x = 31

Substitute this value back into the equation for ∠D:

m∠D = 4(31)+8 = 132°

Since ∠F is a vertical angle with ∠D, ∠F will also have a measure of 132°.

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)

Answer 3

If two angles are complementary, their measures add up to 90 degrees.

Given that m∠A = x° and m∠B = (2x)°, we can set up the equation:

x° + (2x)° = 90°

Combine like terms:

3x° = 90°

Divide both sides by 3:

x° = 30°

Now, substitute this value back into the equation for ∠B:

m∠B = 2(30°) = 60°

Therefore, the measure of ∠B is 60°.

Answer 4

thanks

Answer 5

You're welcome! If you have any more questions, feel free to ask.