To determine if two angles are complementary, their measures must add up to 90 degrees. Let's look at each pair of angles and check if their sum is indeed 90 degrees:
A. 17 and 34 degrees:
First, we calculate the sum of the angles:
[tex]\[ 17 + 34 = 51 \][/tex]
Since 51 is not equal to 90, 17 and 34 degrees are not complementary angles.
B. 30 and 60 degrees:
Next, we calculate the sum of these angles:
[tex]\[ 30 + 60 = 90 \][/tex]
Since 90 is equal to 90, 30 and 60 degrees are complementary angles.
C. 40 and 40 degrees:
We calculate their sum as follows:
[tex]\[ 40 + 40 = 80 \][/tex]
Since 80 is not equal to 90, 40 and 40 degrees are not complementary angles.
D. 15 and 30 degrees:
Lastly, we compute the sum of these angles:
[tex]\[ 15 + 30 = 45 \][/tex]
Since 45 is not equal to 90, 15 and 30 degrees are not complementary angles.
Based on the above calculations, the pair of angles that are complementary is 30 and 60 degrees. Therefore, the measures of the complementary angles are 30 degrees and 60 degrees.
