1 Answer

Cheersmate · Answer 1 · 2022-02-02T13:47:01+0000

Complete the statement :

$\color{plum}\tt2x + 7° = \underline{65} \: degrees$

The exterior angle corollary states that the measure of a triangle's exterior angle is the sum of the opposite interior angles of the exterior angle.

Which means :

Let us solve this equation to find the measure of the exterior angle :

$=\tt 2x + 7 = 36 + x$

$= \tt2x + 7 - x = 36$

$=\tt x + 7 = 36$

$= \tt \: x = 36 - 7$

$=\tt x = 29$

Then, the measure of the exterior angle :

$= \tt2 * 29 + 7$

$= \tt58 + 7$

$= \tt65$

Thus, the measure of the exterior angle 2x+7 = 65°

Let us check whether or not we have found out the correct measure of each angle by placing 29 in the place of x:

$= \tt2 * 29 + 7 = 36 + 29$

$=\tt 58 + 7 = 36 + 29$

$= \tt65 = 65$

Since the measures match we can conclude that we have found out the correct value of each angle.

Therefore, ∠2x + 7° = 65°