Complete the statement :
[tex]\color{plum}\tt2x + 7° = \underline{65} \: degrees[/tex]
Steps to derive the correct solution :
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 :
[tex] =\tt 2x + 7 = 36 + x[/tex]
[tex] = \tt2x + 7 - x = 36[/tex]
[tex] =\tt x + 7 = 36[/tex]
[tex] = \tt \: x = 36 - 7[/tex]
[tex] =\tt x = 29[/tex]
- Thus, the measure of ∠x = 29°
Then, the measure of the exterior angle :
[tex] = \tt2 \times 29 + 7[/tex]
[tex] = \tt58 + 7[/tex]
[tex] = \tt65[/tex]
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:
[tex] = \tt2 \times 29 + 7 = 36 + 29[/tex]
[tex] =\tt 58 + 7 = 36 + 29[/tex]
[tex] = \tt65 = 65[/tex]
Since the measures match we can conclude that we have found out the correct value of each angle.
Therefore, ∠2x + 7° = 65°
