Final answer:
To find the measure of each angle of the triangle, we set up an equation using the given information. After solving the equation, we find the measure of the exterior angle, as well as the measures of the remote interior angles. The measures of the angles in the triangle are 99°, 144°, and -9° (which is discarded since angles cannot have negative measures).
Step-by-step explanation:
To find the measure of each angle of the triangle, we need to use the fact that the sum of the measures of the interior angles of a triangle is always 180 degrees. Let's start by finding the measure of the exterior angle. The exterior angle is equal to the sum of the remote interior angles.
Given that the measures of the remote interior angles are 3x and 45°, we can set up an equation: 4x + 12 = 3x + 45°.
Solving this equation, we get x = 33°. Now we can find the measure of the exterior angle: 4(33°) + 12 = 144°.
Since the exterior angle and the remote interior angles are supplementary (add up to 180 degrees), we can find the measures of the remote interior angles. The first remote interior angle is 3x = 3(33°) = 99°. The second remote interior angle is 180° - 45° - 144° = -9°. However, since angles cannot have negative measures, we discard the -9° and focus on the other two angles: 99° and 144°.
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