Final answer:
The measure of each angle of the triangle is found by solving an equation using the sum of exterior angles.
Step-by-step explanation:
To find the measure of each angle of the triangle, we can use the fact that the sum of the exterior angles of any polygon is always 360 degrees. The measure of the exterior angle of the triangle is given as 4x + 12. Therefore, we have the equation: 4x + 12 + 3x + 45 + 45 = 360. Simplifying the equation, we get 7x + 102 = 360. Solving for x, we find x = 36. Substituting this value back into the equations, we can find the measures of the angles. The exterior angle is 4(36) + 12 = 156 degrees. The measures of the remote interior angles are 3(36) = 108 degrees and 45 degrees.
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