Question

1. write an equation relating the measures of ∠1, ∠2, and ∠3. write another equation relating the measures of ∠1, ∠2, and ∠4.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180 degrees. For the triangle with interior angles $\angle1$, $\angle2$, and $\angle3$, we have $\angle1+\angle2+\angle3 = 180^{\circ}$.

Step2: Use the property of a linear - pair of angles

$\angle3$ and $\angle4$ form a linear - pair of angles. A linear - pair of angles is supplementary, i.e., $\angle3+\angle4=180^{\circ}$. From $\angle1+\angle2+\angle3 = 180^{\circ}$ and $\angle3+\angle4 = 180^{\circ}$, we can get $\angle1+\angle2=\angle4$.

Answer:

Equation relating $\angle1$, $\angle2$, and $\angle3$: $\angle1+\angle2+\angle3 = 180^{\circ}$
Equation relating $\angle1$, $\angle2$, and $\angle4$: $\angle1+\angle2=\angle4$