For triangle XYZ, m∠X = 52°, m∠Y = (3x − 33)°, and m∠Z = (5x − 23)°. Find m∠Y.
a) m∠Y = 157°
b) m∠Y = 71°
c) m∠Y = 41°
d) m∠Y = 36°
To find m∠Y, we need to set up an equation using the fact that the sum of the angles in a triangle is 180°.
m∠X + m∠Y + m∠Z = 180°
Plugging in the given values, we have:
52° + (3x - 33)° + (5x - 23)° = 180°
Simplifying the equation, we get:
52° + 3x - 33° + 5x - 23° = 180°
Combine like terms:
8x - 4° = 180°
8x = 184°
Divide both sides by 8:
x = 23°
Now we can find m∠Y:
m∠Y = 3x - 33°
m∠Y = 3(23°) - 33°
m∠Y = 69° - 33°
m∠Y = 36°
So, the correct answer is:
d) m∠Y = 36°