Question

$\angle 3$ and $\angle 4$ arecomplementary angles, and $m\angle 3=24°$. Find $m\angle 4$.

Short answer

The measure of angle $m\angle 4$ is $66°$.

Step-by-step solution

Step 1. Given Information.

$m\angle 3=24°$

Step 2. Concept used.

If the sum of two angles is $90°$ then the angles are called complementary angles and if the sum is $180°$ then the angles are called supplementary angles.

Step 3. Calculation.

Since $\angle 3$ and $\angle 4$ are complementary angles.

$\begin{array}{c}m\angle 3+m\angle 4=90°\\ 24°+m\angle 4=90°\\ m\angle 4=90°-24°\\ =66°\end{array}$

Step 4. Conclusion.

Therefore, the measure of the angle that is complementary to an angle measuring $24°$ is $66°$.