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 triangle - angle sum property

The sum of the interior angles of a triangle is 180°. In the given triangle with interior angles ∠1, ∠2, and ∠3, we have the equation $\angle1+\angle2+\angle3 = 180^{\circ}$.

Step2: Use exterior - angle property

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles. For the exterior angle ∠4 and non - adjacent interior angles ∠1 and ∠2, we get the equation $\angle4=\angle1 + \angle2$.

Answer:

Equation for ∠1, ∠2, ∠3: $\angle1+\angle2+\angle3 = 180^{\circ}$
Equation for ∠1, ∠2, ∠4: $\angle4=\angle1+\angle2$