Two angles are complementary when the sum of their measures is equal to 90°. Then if we have an angle with a measure of x° and another with a measure of y° and they are complementary we get the following:
[tex]x+y=90[/tex]We are told that A and B are complementary which means that their measures meet the following equation:
[tex]A+B=90[/tex]We also know that A is four times larger than B so we get:
[tex]A=4B[/tex]Then if we replace A with 4B in the first equation we get:
[tex]\begin{gathered} 4B+B=90 \\ 5B=90 \end{gathered}[/tex]Then we divide both sides by 5:
[tex]\begin{gathered} \frac{5B}{5}=\frac{90}{5} \\ B=18 \end{gathered}[/tex]Then, if B is 18° A must be:
[tex]A=4B=4\cdot18=72[/tex]So A=72°. Then the answer is option D.
