Question

find m∠g. p || r. the diagram is not to scale. 34 104 110 146 34°

Explanation:

Step1: Identify angle - relationship

Since $p\parallel r$, the angle adjacent to the $34^{\circ}$ angle and $\angle G$ are corresponding angles. The angle adjacent to the $34^{\circ}$ angle forms a linear - pair with the $34^{\circ}$ angle.

Step2: Calculate the adjacent angle

The sum of angles in a linear - pair is $180^{\circ}$. Let the adjacent angle to the $34^{\circ}$ angle be $x$. Then $x + 34^{\circ}=180^{\circ}$, so $x = 180^{\circ}-34^{\circ}=146^{\circ}$.

Step3: Determine $\angle G$

Because of the corresponding - angles postulate (when two parallel lines are cut by a transversal, corresponding angles are congruent), $\angle G=x$. So $m\angle G = 146^{\circ}$.

Answer:

$146$