Question

1. if m∠2 = 37°, what is m∠3? 2. if m∠2 = 37°, and m∠3 = 10x + 23°, what is the value of x?

Explanation:

Step1: Assume ∠2 and ∠3 are supplementary

Supplementary angles sum to 180°. So, $m\angle2 + m\angle3=180^{\circ}$.

Step2: Substitute given angle - measures

Given $m\angle2 = 37^{\circ}$ and $m\angle3=10x + 23^{\circ}$, we substitute into the equation: $37+(10x + 23)=180$.

Step3: Simplify the left - hand side

First, combine like terms: $37+23+10x=180$, which gives $60 + 10x=180$.

Step4: Solve for x

Subtract 60 from both sides: $10x=180 - 60$, so $10x=120$. Then divide both sides by 10: $x=\frac{120}{10}=12$.

Answer:

$x = 12$