Find the measure of the angle indicated, WILL GIVE
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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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