Question

to find out if the sum of the three interior - angle measures of any triangle is 180°, show: m∠1 + m∠2 + m∠3 = 180°. m∠1 = m∠4, m∠2 = m∠5. rewrite the angle sum by substituting for m∠1 and m∠2. m∠1 + m∠2 + m∠3 =? +? + m∠3

Explanation:

Step1: Use angle - relationship

We know that $\angle1$ and $\angle4$ are vertical - angles, so $m\angle1 = m\angle4$. Also, $\angle2$ and $\angle5$ are vertical - angles, so $m\angle2 = m\angle5$.

Step2: Substitute into angle - sum formula

The sum of the interior angles of a triangle is $m\angle1 + m\angle2 + m\angle3=180^{\circ}$. Substituting $m\angle1 = m\angle4$ and $m\angle2 = m\angle5$ into the formula, we get $m\angle4 + m\angle5 + m\angle3 = 180^{\circ}$.

Answer:

$m\angle4 + m\angle5 + m\angle3 = 180^{\circ}$