Question

consider the figure below. given: $angle a = 6x + 20$, $angle b = 4x - 4$. find the degree measure of $angle a$. your answer could be a decimal. answer

Explanation:

Step1: Note angle relationship

Since $\angle A$ and $\angle B$ are complementary (right - angle shown), $\angle A+\angle B = 90^{\circ}$.

Step2: Substitute angle expressions

Substitute $\angle A=6x + 20$ and $\angle B = 4x-4$ into $\angle A+\angle B=90$. So, $(6x + 20)+(4x-4)=90$.

Step3: Simplify the equation

Combine like - terms: $6x+4x+20 - 4=90$, which gives $10x+16 = 90$.

Step4: Solve for x

Subtract 16 from both sides: $10x=90 - 16=74$. Then divide both sides by 10: $x=\frac{74}{10}=7.4$.

Step5: Find measure of $\angle A$

Substitute $x = 7.4$ into the expression for $\angle A$: $\angle A=6x + 20=6\times7.4+20$.
$\angle A=44.4+20=64.4$.

Answer:

$64.4$