Question

the sum of the interior angle measures of a triangle must be °. so, m∠1 + m∠3 + m∠4 = 180°. we are given that m∠1 = 62°. so, m∠3 + m∠4 = 118°. from the figure, we can see that m∠1 + m∠2 = 242°. since m∠1 = 62°, it must be that m∠2 = 34°. therefore, m∠2 > m∠3 + m∠4. this result is an example of the exterior angle property of triangles. for any triangle, the measure of an exterior angle is greater than the sum of the measures of its two remote interior angles.

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles of a triangle is $180^{\circ}$. Given $\angle1+\angle3+\angle4 = 180^{\circ}$ and $\angle1 = 62^{\circ}$, we find $\angle3+\angle4$ by subtraction.
$180 - 62=118^{\circ}$

Step2: Find the measure of $\angle2$

Given $\angle1+\angle2 = 242^{\circ}$ and $\angle1 = 62^{\circ}$, we find $\angle2$ by subtraction.
$242 - 62 = 180^{\circ}$ (There is an error in the original text where it says $\angle2 = 34^{\circ}$. The correct calculation is $242-62 = 180^{\circ}$)

Step3: Compare $\angle2$ and $\angle3+\angle4$

Since $\angle2=180^{\circ}$ and $\angle3 + \angle4=118^{\circ}$, we have $\angle2>\angle3+\angle4$. This is an example of the Exterior - Angle Property of Triangles which states that the measure of an exterior angle is greater than the sum of the measures of its two remote interior angles.

Answer:

The measure of an exterior angle is greater than the sum of the measures of its two remote interior angles.