The Triangle Exterior Angle Postulate states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
In the given problem, the exterior angle is < JDC, and its measure is equal to the sum of the measures of < (12x -3)° and < 32°.
We can set up the following equality statement to solve for the value of x, and find out the measure of < JDC:
m < JDC° = < (12x -3)° + < 32°
< (8 + 15x)° = < (12x -3)° + < 32°
Subtract 8 from both sides:
8 - 8 + 15x = 12x - 3 + 32 - 8
15x = 12x + 21
Subtract 12x from both sides:
15x - 12x = 12x - 12x + 21
3x = 21
Divide both sides by 3 to solve for x:
3x/3 = 21/3
x = 7
To verify whether the value for x is correct, substitute x = 7 into the equality statement:
m < JDC° = < (12x -3)° + < 32°
< (8 + 15x)° = < (12x -3)° + < 32°
[8 + 15(7)]° = [12(7) - 3]° + 32°
8° + 105° = 81° + 32°
113° = 113° (True statement). Therefore, the correct value for x = 7.
Therefore, the correct answer is C) m < JDC = 113°.
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