Question

exercise #4: it is given that ∠a and ∠b are complementary. if the measure of ∠b is 15 more than twice the measure of ∠a, determine the measure of both angles algebraically.

Explanation:

Step1: Set up equations

Let the measure of $\angle A=x$. Since $\angle B$ is 15 more than twice the measure of $\angle A$, the measure of $\angle B = 2x + 15$. And because $\angle A$ and $\angle B$ are complementary, $x+(2x + 15)=90$.

Step2: Simplify the equation

Combine like - terms: $3x+15 = 90$.

Step3: Solve for $x$

Subtract 15 from both sides: $3x=90 - 15=75$. Then divide both sides by 3, so $x = 25$.

Step4: Find the measure of $\angle B$

Substitute $x = 25$ into the expression for $\angle B$. $\angle B=2x + 15=2\times25+15=50 + 15=65$.

Answer:

The measure of $\angle A$ is $25^{\circ}$ and the measure of $\angle B$ is $65^{\circ}$.