Question

1. suppose ∠a and ∠b are supplementary angles, m∠a=(3x + 5)°, and m∠b=(2x - 10)°. solve for x and then find m∠a and m∠b.

Explanation:

Step1: Use supplementary - angle property

Since $\angle A$ and $\angle B$ are supplementary, $m\angle A + m\angle B=180^{\circ}$. So, $(3x + 5)+(2x-10)=180$.

Step2: Simplify the left - hand side

Combine like terms: $3x+2x + 5-10=180$, which gives $5x-5 = 180$.

Step3: Isolate the variable term

Add 5 to both sides of the equation: $5x-5 + 5=180 + 5$, resulting in $5x=185$.

Step4: Solve for x

Divide both sides by 5: $\frac{5x}{5}=\frac{185}{5}$, so $x = 37$.

Step5: Find $m\angle A$

Substitute $x = 37$ into the expression for $m\angle A$: $m\angle A=(3x + 5)^{\circ}=(3\times37 + 5)^{\circ}=(111 + 5)^{\circ}=116^{\circ}$.

Step6: Find $m\angle B$

Substitute $x = 37$ into the expression for $m\angle B$: $m\angle B=(2x-10)^{\circ}=(2\times37-10)^{\circ}=(74 - 10)^{\circ}=64^{\circ}$.

Answer:

$x = 37$, $m\angle A=116^{\circ}$, $m\angle B = 64^{\circ}$