Question

the measure of angle 1's complementary angle is 1/4 times as many as the measure of angle 1's supplementary angle. angle 1 = ?°

Answer 1

The measure of angle 1 is 60 degrees, derived by setting up an equation that relates its complementary and supplementary angles and solving for the angle's measure.

Step-by-step explanation:

The given problem involves finding the measure of angle 1 given the relationship between its complementary and supplementary angles. Complementary angles sum up to 90 degrees, while supplementary angles sum up to 180 degrees. Thus, if x is the measure of angle 1, the measure of its complementary angle is 90 - x, and the measure of its supplementary angle is 180 - x. The problem states that the complementary angle is 1/4 times as many as the supplementary angle, which gives us the equation:

90 - x = 1/4 (180 - x)

Expanding and solving for x:

90 - x = 45 - 1/4x

Combining like terms:

45 = 3/4x

Multiplying both sides by 4/3 to solve for x:

x = 60

The measure of angle 1 is therefore 60 degrees.