Question

An angle measures 66° more than the measure of its complementary angle what is the measure of each angle

Answer 1

Answer:

The measures of the two angles are 12° and 78°

Step-by-step explanation:

Let us explain what is the complementary angles

Two angles are complementary if the sum of their measures is 90°

Example:

If m∠x + m∠y = 90°, then

∠x and ∠y are complementary angles

Let us solve the question

Assume that the measure of one of the complementary angle is x°

∵ The measure of its complementary is 66° more than it

∴ The measure of its complementary = x + 66

∵ The sum of the measures of the complementary angles is 90°

∴ x + 66 + x = 90

→ Add the like terms in the left side

∴ 2x + 66 = 90

→ Subtract 66 from both sides

∴ 2x + 66 - 66 = 90 - 66

∴ 2x = 24

→ Divide both sides by 2

∴ $\frac{2x}{2}=\frac{24}{2}$

∴ x = 12°

→ Substitute the value of x in the second angle to find x

∵ The measure of the other angle = 12 + 66

∴ The measure of the other angle = 78°

∴ The measures of the two angles are 12° and 78°