## anonymous 5 years ago 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?

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.