Answer:
Angle T = 62°; Angle U = 43°; Angle V = 75°
Explanation:
First, find x. We know that the interior angles of a triangle will always add up to 180°.
180° = (5x +2)° + (6x + 3)° + (2x + 19)° –––Combine like terms
180° = 13x + 24 –––Subtract 24 from both sides
156° = 13x ––– Divide both sides by 13 to get x alone
12° = x
Now that we know what x is, we can substitute it in the expressions for the angles.
Angle T:
5x +2
5(12) + 2
60 +2
62°
Angle U:
2x + 19
2(12) + 19
24 + 19
43°
Angle V:
6x + 3
6(12) + 3
72 + 3
75°
Check:
They must equal 180° when added together:
75° + 62° + 43° = 180°
75° + 105° = 180°
180° = 180°