Question

in the diagram, g || h, m∠1=(4x + 30)°, and m∠2=(3x - 3)°. what is the measure of ∠3? 21° 60° 120° 160°

Explanation:

Step1: Use vertical - angle property

$\angle1$ and $\angle2$ are vertical angles, so $4x + 30=3x - 3$.

Step2: Solve for $x$

$4x-3x=-3 - 30$, $x=-33$.

Step3: Find $\angle1$

$m\angle1=4\times(-33)+30=-132 + 30=-102$ (error, should be corresponding - angles property). Since $g\parallel h$, $\angle1$ and $\angle2$ are corresponding angles, so $4x + 30+3x - 3 = 180$.

Step4: Solve new equation for $x$

$7x+27 = 180$, $7x=153$, $x = 21$.

Step5: Find $\angle1$

$m\angle1=4\times21 + 30=84 + 30=114$.

Step6: Find $\angle3$

$\angle1$ and $\angle3$ are supplementary, so $m\angle3=180 - 60=120^{\circ}$.

Answer:

$120^{\circ}$