Answer:
The measures of the 3 angles are:
Angle T = 69°
Angle U = 36°
Angle V = 75°
Step-by-step explanation:
The Triangle Sum Theorem states that the 3 angles of a triangle must add up to 180°.
We don't know the angles of the triangle, but we do know that the sum of all three unknown angles is 180°.
We set the three expressions together as equal to 180°.
6x + 3 + 6x + 9 + 2x + 14 = 180
Simplify
14x + 26 = 180
Subtract 26
14x = 154
x = 11
Now, we check our answer for x.
6(11) + 3 + 6(11) + 9 + 2(11) + 14 = 180
69 (measure of angle T) + 75 (measure of angle V) + 36 (measure of angle U) = 180
180 = 180 ✅
Note that once we found x, would substitute it in and get the needed measures. Since the needed measures add up to 180°, we know that our answer is correct.
The measures of the 3 angles are:
Angle T = 69°
Angle U = 36°
Angle V = 75°
