Find the measures of the two angles
A. 8 degrees and 82 degrees
B. Both are 45 degrees
C. 10 degrees and 80 degrees
D. 38 degrees and 52 degrees
The answer is option A. The sum of the measures of the angles in any triangle is always 180 degrees. In this case, the sum of the two angles is 8 degrees + 82 degrees = 90 degrees. Therefore, if we add a third angle to form a triangle, that angle must measure 180 degrees - 90 degrees = 90 degrees. This means that we have a right triangle, and the two given angles are the measures of its two acute angles.
To find the measures of the two angles, we need to identify which option corresponds to the measures of the two angles.
A. 8 degrees and 82 degrees
B. Both are 45 degrees
C. 10 degrees and 80 degrees
D. 38 degrees and 52 degrees
The correct option is D. The measures of the two angles are 38 degrees and 52 degrees.
To find the measures of the two angles, you need to look at the options given and match them with the sum of two angles that equals 90 degrees. The sum of two angles in a right angle is always 90 degrees.
Let's go through the options one by one:
A. 8 degrees and 82 degrees
Sum of 8 degrees and 82 degrees is 8 + 82 = 90 degrees. So, option A is correct.
B. Both are 45 degrees
The sum of two 45-degree angles is 45 + 45 = 90 degrees. So, option B is also correct.
C. 10 degrees and 80 degrees
The sum of 10 degrees and 80 degrees is 10 + 80 = 90 degrees. Thus, option C is correct as well.
D. 38 degrees and 52 degrees
The sum of 38 degrees and 52 degrees is 38 + 52 = 90 degrees. Hence, option D is correct.
Therefore, all of the given options result in a sum of 90 degrees, so all of them are correct.