Question

TWO ANGLES ARE COMPLEMENTARY. THE SUM OF THE MEASURE OF THE FIRST ANGLE AND ONE-FOURTH THE SECOND ANGLE 77.55 DEGREE.

FIND THE MEASURE OF THE ANGLES?
WHAT IS THE MEASURE OF THE SMALLER ANGLE?

Answer 1

Let x and y be the first and the second angle respectively. Then:
\[x+y=90 \rightarrow(1)\]
\[x+{1 \over 4}y=77.55 \rightarrow(2)\]
Subtract (2) from (1), you get:
\[{3 \over 4}y=12.45 \implies y=12.45({4 \over 3}) \implies y=16.6\]
Substitute this value for y in equation (1), you get:
\[x+16.6=90 \implies x=73.4\]
So the first angle is 73.4 degrees and the second angle is 16.6 degrees.