For triangle XYZ, m∠X = 47°, m∠Y = (2x − 18)°, and m∠Z = (5x − 45)°. Find m∠Y.
a m∠Y = 28°
b m∠Y = 38°
c m∠Y = 95°
d m∠Y = 142°
We know that the sum of the angles in a triangle is 180°. So, we have the equation:
47 + (2x - 18) + (5x - 45) = 180
Combining like terms, we get:
7x - 16 = 180
Adding 16 to both sides, we have:
7x = 196
Dividing both sides by 7, we get:
x = 28
Now that we know the value of x, we can substitute it back into the equation for m∠Y:
m∠Y = 2x - 18 = 2(28) - 18 = 56 - 18 = 38
Therefore, m∠Y = 38°.
The correct answer is b) m∠Y = 38°.