Two angles are complementary. The larger angle is 6° less than five times the measure of the smaller angles. What is the measure of the larger angle?

Correct option is C

​Given:

Two angles are complementary (sum=90^∘).

Larger angle = $$5 \times \text{Smaller angle} - 6^\circ$$​​

Formula Used:

​$$\text{Smaller angle} + \text{Larger angle} = 90^\circ$$​​

Solution:

Let the smaller angle be x:

x + (5x - 6) = 90

​$$6x - 6 = 90 \\ \ \\ \Rightarrow \quad 6x = 96 \\ \ \\ \Rightarrow \quad x = 16^\circ$$​​

Larger angle:

​$$5x - 6 = 5(16) - 6 = 80 - 6 = 74^\circ$$​​