Question

complementary angles are two angles that have measures with a sum of 90°. angles p and q are complementary and the measure of angle p is 6° more than twice the measure of angle q. write a system of equations and use substitution to find the measures of angles p and q.

Explanation:

Step1: Set up equations

Let the measure of angle $Q$ be $x$ and the measure of angle $P$ be $y$. Since $P$ and $Q$ are complementary, $x + y=90$. Also, since the measure of angle $P$ is 6 more than twice the measure of angle $Q$, $y = 2x+6$.

Step2: Substitute

Substitute $y = 2x + 6$ into $x + y=90$. We get $x+(2x + 6)=90$.

Step3: Simplify the equation

Combine like - terms: $3x+6 = 90$. Subtract 6 from both sides: $3x=90 - 6=84$.

Step4: Solve for $x$

Divide both sides by 3: $x=\frac{84}{3}=28$.

Step5: Solve for $y$

Substitute $x = 28$ into $y = 2x+6$. Then $y=2\times28 + 6=56 + 6=62$.

Answer:

The measure of angle $Q$ is $28^{\circ}$ and the measure of angle $P$ is $62^{\circ}$.