Question

question 6 (1 point)
∠a and ∠b are supplementary angles. find m∠a and m∠b.
m∠a=(x + 11)°
m∠b=(x - 15)°
m∠a = _____
m∠b = _____
blank 1:
blank 2:

Explanation:

Step1: Use supplementary - angle property

Since $\angle A$ and $\angle B$ are supplementary, $m\angle A + m\angle B=180^{\circ}$. So, $(x + 11)+(x - 15)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+11+x - 15=2x-4$. So, $2x-4 = 180$.

Step3: Solve for $x$

Add 4 to both sides: $2x=180 + 4=184$. Then divide both sides by 2: $x=\frac{184}{2}=92$.

Step4: Find $m\angle A$

Substitute $x = 92$ into the expression for $m\angle A$: $m\angle A=(x + 11)^{\circ}=(92+11)^{\circ}=103^{\circ}$.

Step5: Find $m\angle B$

Substitute $x = 92$ into the expression for $m\angle B$: $m\angle B=(x - 15)^{\circ}=(92-15)^{\circ}=77^{\circ}$.

Answer:

$m\angle A = 103$
$m\angle B = 77$