Question

Angles A and B are complementary and in ratio of 3:6. What is the measure of each angle

Answer 1

complementary angles add up to 90°, so therefore we know that ∡A + ∡B = 90°, and also they are in a ratio of 3:6.

$\bf \cfrac{A}{B}=\cfrac{3}{6}\implies \cfrac{A}{B}=\cfrac{1}{2}\implies 2A=\boxed{B} \\\\[-0.35em] ~\dotfill\\\\ A+B=90\implies A+\boxed{2A}=90\implies 3A=90\\\\\\ A=\cfrac{90}{3}\implies \blacktriangleright A=30 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 2(30)=B\implies \blacktriangleright 60=B \blacktriangleleft$