Question

1. two angles are complementary. the sum of the first angle plus twice the second angle is 165°. find the measures of the angles.

Explanation:

Step1: Define variables

Let the first angle be $x$ and the second angle be $y$. Since they are complementary, $x + y=90^{\circ}$, so $x = 90 - y$.

Step2: Set up second - equation

The sum of the first angle plus twice the second angle is $165^{\circ}$, so $x + 2y=165$.

Step3: Substitute $x$

Substitute $x = 90 - y$ into $x + 2y=165$. We get $(90 - y)+2y=165$.

Step4: Solve for $y$

Simplify the left - hand side: $90 - y+2y=90 + y$. Then $90 + y=165$. Subtract 90 from both sides: $y=165 - 90=75^{\circ}$.

Step5: Solve for $x$

Substitute $y = 75$ into $x = 90 - y$. So $x=90 - 75 = 15^{\circ}$.

Answer:

The first angle is $15^{\circ}$ and the second angle is $75^{\circ}$.