Angle X and angle Y are complementary angles. The measure of angle Y is 6 less than twice the measure of angle X . What is the measure of each angle?
The correct answer and explanation is:
Let’s define the measures of angle X and angle Y.
We are told that angle X and angle Y are complementary, meaning their sum is 90 degrees: X+Y=90X + Y = 90
Also, we know that angle Y is 6 degrees less than twice the measure of angle X: Y=2X−6Y = 2X – 6
Now, substitute the second equation into the first equation: X+(2X−6)=90X + (2X – 6) = 90
Simplify: 3X−6=903X – 6 = 90
Add 6 to both sides: 3X=963X = 96
Now, divide both sides by 3: X=32X = 32
Now that we know the measure of angle X is 32 degrees, substitute this value back into the equation for Y: Y=2(32)−6=64−6=58Y = 2(32) – 6 = 64 – 6 = 58
Therefore, the measure of angle X is 32 degrees, and the measure of angle Y is 58 degrees.
Explanation:
Since complementary angles sum up to 90 degrees, we can use this property to set up an equation. We also used the relationship that angle Y is 6 less than twice the measure of angle X to create a second equation. By solving the system of equations, we found that angle X is 32 degrees, and angle Y is 58 degrees.