Question

Hi, having trouble understanding this question.. as well as solving it.

Angle P and angle Q are complementary angles. The measure of angle P is one-fourth the measure of angle Q. Find the measure of each angle.

The measure of angle P is _________.

The measure of angle Q is _________.

Answer 1

The measure of angle P and Q is given in the picture.

Answer 2

-- You have two angles.

-- They're complementary . . . they add up to 90 degrees.

-- One is 4 times as big as the other one.
___________________________________________

-- The smaller angle has 1 share of the 90 degrees.

-- The bigger angle has 4 shares of the 90 degrees.

-- (The smaller one is 1/4 the size of the bigger one.
The bigger one is 4 times the size of the smaller one.)

-- When you add them together, you get 5 shares, totaling 90 degrees.

-- What's the size of each share ? It's 90/5 = 18 degrees.

-- The smaller angle gets one share . . . 18 degrees.

-- The bigger angle gets 4 shares. (4 x 18) = 72 degrees.
____________________________________

Check:

-- Is the small one 1/4 the size of the big one ? 18/72 = 1/4 Yes.

-- Are they complementary ? Do they add up to 90 degrees ?

18 + 72 = 90 Yes.

yay !