Answer:
m < S = 40°
Step-by-step explanation:
According to the Triangle Exterior Angle Postulate, the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
The exterior angle is m < R = 140°. In reference to the Triangle Exterior Angle Postulate, the sum of the measures of < T and < S must equal 140°.
Given m < T = (8x + 4)°
m < S = (3x + 4)°
We can set up the following equality statement to solve for the value of x:
m < R = m < T + m < S
140° = (8x + 4)° + (3x + 4)°
Combine like terms:
140° = 11x + 8
Subtract 8 from both sides:
140° - 8 = 11x + 8 - 8
132° = 11x
Divide both sides by 11:
132°/11 = 11x/11
12 = x
Substitute the value of x into the equality statement to verify whether it is the correct value:
140° = (8x + 4)° + (3x + 4)°
140° = [8(12) + 4]° + [3(12) + 4]°
140° = (96 + 4)° + (36 + 4)°
140° = 100° + 40°
140° = 140° (True statement. Therefore, the correct value for x = 12).
Therefore, m < S = (3x + 4)° = [3(12) + 4]° = 40°
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