Answer: m∠R = 101°, m∠P = 56°, and m∠Q = 23°
Step-by-step explanation:
The sum of a triangle's interior angles is equal to 180 degrees. Using this information, we will add all of the angles together and set it equal to 180° to solve for x.
Equation:
7x° - 11° + 3x° + 8° + x° + 7° = 180°
Combine like terms:
11x° + 4° = 180°
Subtract 4 from both sides of the equation:
11x° = 176°
Divide both sides of the equation by 11°:
x = 16
Substitute this back into the expression for each angle.
m∠R = 7x° - 11° = 7(16)° - 11° = 101°
m∠P = 3x° + 8° = 3(16)° + 8° = 56°
m∠Q = x° + 7° = (16)° + 7° = 23°
