Question

The measure of an angle is twice the measure of its compliment. I hat are the measures of both angles?

A) 30 and 60
B) 20 and 40
C) 45 and 45
D) 60 and 120

Answer 1

If angles are complementary then their sum is 90 degrees.

`\alpha+\beta=90^(\circ)`.

If one is twice the other we get,

`2\beta + \beta=3\beta=90^(\circ)\implies \beta=(90^(\circ))/(3)=\boxed{30^(\circ)}`

And,

`\alpha+30^(\circ)=90^(\circ)\implies\alpha=90^(\circ)-30^(\circ)=\boxed{60^(\circ)}`.

So the answer is A. 30 and 60.

Hope this helps.