Answer: 133
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Explanation:
The quickest way to get this answer is to add the angles given to get 87+46 = 133
This is through the use of the remote interior angle theorem.
Note how the angles 87 and 46 are interior, or inside the triangle. And also, they are not adjacent to the exterior angle we want to find. So that's where the "remote" portion comes in.
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The slightly longer method involves letting x be the measure of the missing interior angle of the triangle.
The three interior angles add to 180
87+46+x = 180
133+x = 180
x = 180 - 133
x = 47
The missing interior angle of the triangle is 47 degrees.
Angle 1 is adjacent and supplementary to this 47 degree angle, so,
(angle1)+(47) = 180
angle1 = 180-47
angle1 = 133 degrees
This example helps confirm that the remote interior angle theorem is correct.
