Question

one angle is twice its complement increased by 30°. find the measure of the two complementary angles. recall that two angles are said to be complementary angles if they add up to 90°.

Explanation:

Step1: Let the angle be $x$

Let the measure of one angle be $x$. Then its complement is $90 - x$.

Step2: Set up the equation

According to the problem, $x=2(90 - x)+30$.

Step3: Expand the right - hand side

Expand $2(90 - x)+30$ to get $180-2x + 30=210-2x$. So the equation becomes $x=210 - 2x$.

Step4: Solve for $x$

Add $2x$ to both sides: $x + 2x=210$, which simplifies to $3x=210$. Then divide both sides by 3: $x = 70$.

Step5: Find the complement

The complement of $x$ is $90 - x$. Substitute $x = 70$ into it, we get $90-70 = 20$.

Answer:

The two complementary angles are $70^{\circ}$ and $20^{\circ}$.