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 27.5°. correct answer: 27.5°. part 2 of 2 the larger angle is

Explanation:

Step1: Define the relationship

Let the smaller angle be $x$ and the larger angle be $y$. We know that complementary angles sum to 90 degrees, so $x + y=90$. Also, $y = 3x- 20$.

Step2: Substitute and solve for $x$

Substitute $y = 3x - 20$ into $x + y=90$. We get $x+(3x - 20)=90$. Combine like - terms: $4x-20 = 90$. Add 20 to both sides: $4x=90 + 20=110$. Then divide both sides by 4: $x=\frac{110}{4}=27.5$.

Step3: Solve for $y$

Substitute $x = 27.5$ into $x + y=90$. So $y=90 - 27.5 = 62.5$.

Answer:

$62.5$