Question

in the diagram, g // h, m∠1=(4x + 36)°, and m∠2=(3x - 3)°. what is the measure of ∠3? 21° 60° 120° 159°

Explanation:

Step1: Use vertical - angle property

Since $\angle1$ and $\angle2$ are vertical angles, $m\angle1 = m\angle2$. So, $4x + 36=3x - 3$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $4x-3x + 36=3x-3x - 3$, which gives $x+36=-3$. Then subtract 36 from both sides: $x=-3 - 36=-39$.

Step3: Find $m\angle1$ or $m\angle2$

Substitute $x = - 39$ into the expression for $m\angle1$: $m\angle1=4(-39)+36=-156 + 36=-120$. This is wrong. Let's assume $\angle1$ and $\angle2$ are supplementary (since they seem to be on a straight - line). So, $m\angle1+m\angle2 = 180$. Then $(4x + 36)+(3x - 3)=180$.

Step4: Combine like terms

$4x+3x+36 - 3=180$, which simplifies to $7x+33 = 180$.

Step5: Solve for $x$

Subtract 33 from both sides: $7x=180 - 33 = 147$. Then divide both sides by 7: $x = 21$.

Step6: Find $m\angle1$

$m\angle1=4x + 36=4\times21+36=84 + 36=120$.

Step7: Find $m\angle3$

$\angle1$ and $\angle3$ are vertical angles. So, $m\angle3=m\angle1 = 120^{\circ}$.

Answer:

$120^{\circ}$