Question

∠a and ∠b are supplementary angles. find m∠a and m∠b. m∠a = (-3x + 90)° m∠b = (-5x + 150)° m∠a = ____. m∠b = ____. blank 1: blank 2: question 7 (1 point)

Explanation:

Step1: Use supplementary - angle property

Since $\angle A$ and $\angle B$ are supplementary, $m\angle A + m\angle B=180^{\circ}$. So, $(-3x + 90)+(-5x + 150)=180$.

Step2: Simplify the left - hand side

Combine like terms: $-3x-5x + 90+150=180$, which gives $-8x+240 = 180$.

Step3: Solve for $x$

Subtract 240 from both sides: $-8x=180 - 240=-60$. Then divide both sides by - 8, $x=\frac{-60}{-8}=\frac{15}{2}=7.5$.

Step4: Find $m\angle A$

Substitute $x = 7.5$ into the formula for $m\angle A$: $m\angle A=-3\times7.5 + 90=-22.5+90 = 67.5^{\circ}$.

Step5: Find $m\angle B$

Substitute $x = 7.5$ into the formula for $m\angle B$: $m\angle B=-5\times7.5 + 150=-37.5+150 = 112.5^{\circ}$.

Answer:

Blank 1: $67.5$
Blank 2: $112.5$