Question

two angles are complementary. one angle is 20° less than three times the other angle. find the measures of the angles. part 1 of 2 the smaller angle is

Explanation:

Step1: Define the angles

Let one angle be $x$ and the other be $y$. We know that $x + y=180^{\circ}$ (since they are supplementary), and $x = 3y - 20^{\circ}$.

Step2: Substitute and solve

Substitute $x = 3y - 20^{\circ}$ into $x + y=180^{\circ}$. We get $(3y - 20^{\circ})+y = 180^{\circ}$. Combine like - terms: $4y-20^{\circ}=180^{\circ}$. Add $20^{\circ}$ to both sides: $4y=200^{\circ}$. Divide both sides by 4: $y = 50^{\circ}$.

Step3: Find the other angle

Substitute $y = 50^{\circ}$ into $x = 3y - 20^{\circ}$. Then $x=3\times50^{\circ}-20^{\circ}=150^{\circ}-20^{\circ}=130^{\circ}$. The smaller angle is $50^{\circ}$.

Answer:

$50$