Question

In geometry, two angles that sum to 90 degrees are called complementary angles. If the second of two complementary angles is 51 degrees smaller than 2 times the first angle, find the degree measure of both angles.

Answer 1

To determine the degree measure of two complementary angles, set up an equation with the given relationships, solve for x, and then find both angles. The first angle measures 47 degrees, and the second angle is 42 degrees.

Step-by-step explanation:

In geometry, two angles that sum to 90 degrees are known as complementary angles. To solve for the degree measure of both angles when given that the second angle is 51 degrees smaller than twice the first angle, we can use algebra to set up the equation. Let x represent the first angle, then the second angle would be 2x - 51. Since they are complementary, their sum is 90 degrees, which gives us the equation x + (2x - 51) = 90. Solving for x, we get:

1. x + 2x - 51 = 90
2. 3x - 51 = 90
3. 3x = 90 + 51
4. 3x = 141
5. x = 47 degrees

Now, we find the second angle:

2x - 51 = 2(47) - 51 = 93 - 51 = 42 degrees

Therefore, the first angle measures 47 degrees and the second angle measures 42 degrees.