Question

Two angles are complementary is the sum of their measures is 90 degrees. The measure of the first angle is 12 degrees more than 4 times the second angle. Find the measure of the first angle. A. The measure of the first angle is 81.6 degrees. B. The measure of the first angle is 74.4 degrees. C. The measure of the first angle is 8.4 degrees. D. The measure of the first angle is 15.6 degrees.

Answer 1

Answer: The measure of the first angle is 74.4 degrees.

Explanation:

Let x be measure of the first angle and y be the measure of the second angle .

As per given , we have

`x+y=90-----------(1)\\\\ x=12+4y--------(2)`

Substitute the value of x from (2) in equation (1), we get

`12+4y+y=90\\\\ 5y=90-12\\\\ 5y=78\\\\ y=(78)/(5)=15.6`

Put y= 15.6 in (2), we get

`x=12+4(15.6)=74.4`

That means The measure of the first angle is 74.4 degrees.

Correct answer : The measure of the first angle is 74.4 degrees.