Question

the measure of an angle is 87°. what is the measure of its complementary angle?

Explanation:

Step1: Recall the definition of complementary angles.

Complementary angles are two angles whose sum is \( 90^\circ \). Let the given angle be \( \theta = 87^\circ \) and the complementary angle be \( x \). Then we have the equation \( \theta + x=90^\circ \).

Step2: Solve for the complementary angle.

Substitute \( \theta = 87^\circ \) into the equation: \( 87^\circ+x = 90^\circ \). To find \( x \), we subtract \( 87^\circ \) from both sides of the equation: \( x=90^\circ - 87^\circ \).

Step3: Calculate the result.

\( 90^\circ- 87^\circ=3^\circ \).

Answer:

The measure of the complementary angle is \( 3^\circ \).