Answer:
The smaller angle is 20 degrees.
Step-by-step explanation:
Complementary angles are two angles (or more) whose sum is 90 degrees.
If two angles have a sum of 90 degrees and their ratio is 2:7, we must determine which two numbers when added together would yield this proportion?
60 + 30 = 90 but 60:30 is a 6:3 ratio which simplifies to 2:1.
45 + 45 = 90 but 45:45 is a 1:1 ratio.
50:40 = 90 but 50:40 is a 5:4 ratio.
10 + 80 = 90, but 10:80 is a 1:8 ratio. We're getting closer!
20 + 70 = 90, and 20:70 can be simplified to 2:7 when you divide each number in the ratio their greatest common factor (GCF) of 10.
Therefore, the two complementary angles would be 20° and 70°, the smaller of which would be 20°