Question

Can the measure of a complement of an angle ever equal exactly half the measure of a supplement of the angle? Explain.

Short answer

Yes, the measure of a complement of an angle can ever equal exactly half the measure of a supplement of the angle if the measure of the angle is 0°.

Step-by-step solution

Step 1. Description of step.

Consider the measure of the angle be x.

Therefore, the supplement of the angle is$180-x$ and the complement of the angle is $90-x$.

Step 2. Write an equation satisfying the given statement.

The given statement is : The measure of a complement of an angle is exactly equal half the measure of a supplement of the angle.

Therefore, the equation satisfying the given statement is:

$90-x=\frac{1}{2}\left(180-x\right)$

Step 3. Find the value of x.

Solve the above equation to find the value of x.

Therefore,

$$\begin{gathered} 90-x=\frac{1}{2}\left(180-x\right) \\ 2\left(90-x\right)=180-x \\ 180-2x=180-x \\ 180-180=2x-x \\ 0=x \end{gathered}$$

Therefore, the value of x is 0.

Step 4. Find the measure of the angle.

As the value of x is 0 and the measure of the angle is x.

Therefore, the measure of the angle is 0°.

Step 5. Write the conclusion.

The conclusion is that if the measure of the angle is 0°, then the measure of the complement of an angle is exactly half the measure of the supplement of the angle.

Therefore,Yes, the measure of a complement of an angle can ever equal exactly half the measure of a supplement of the angle if the measure of the angle is0°.