Question

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

Answer 1

-- You have two angles.

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

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

Answer 2

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