Question

In ASTU, SU is extended through point U to point V, m/UST = (2 5)°, m/STU = (2x 16)°, and m/TUV = (6x - 9)°. Find m/STU.

a) 24°
b) 32°
c) 40°
d) 48°

Answer 1

To find the measure of angle STU, subtract the given angles from the sum of the angles in a triangle. Solve for x to substitute it into the equation for m/STU.

Step-by-step explanation:

To find the measure of angle STU, we need to use the fact that the sum of the angles in a triangle is 180 degrees. We are given that m/UST = (25)° and m/TUV = (6x - 9)°. We can subtract those two angles from 180 degrees to find the measure of angle STU. So, we have:

m/STU = 180 - m/UST - m/TUV

m/STU = 180 - (25) - (6x - 9)

m/STU = 180 - 25 - 6x + 9

m/STU = 164 - 6x

We can now substitute the given value of m/STU as (2x 16)° and solve for x:

164 - 6x = 2x + 16

164 = 2x + 16 + 6x

164 = 8x + 16

148 = 8x

x = 18.5

Now that we have the value of x, we can substitute it back into the equation for m/STU:

m/STU = 164 - 6(18.5)

m/STU = 164 - 111

m/STU = 53

Therefore, m/STU is 53 degrees.