The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles.
x + 2x-45 = 90
To find the measure of both angles, let's represent the measure of one small angle as x and the measure of the other small angle as y.
According to the problem, we know that one of the small angles is 45 less than twice the measure of the other small angle. This can be written as:
x = 2y - 45
In a right triangle, the sum of the two small angles is always 90 degrees. So we have the equation:
x + y = 90
Now we can solve the system of equations to find the values of x and y.
Substitute the value of x from the first equation into the second equation:
(2y - 45) + y = 90
Combine like terms:
3y - 45 = 90
Add 45 to both sides of the equation:
3y = 135
Divide both sides of the equation by 3:
y = 45
Now substitute the value of y back into the first equation to find x:
x = 2(45) - 45
Simplify:
x = 90 - 45
x = 45
Therefore, the measure of the two small angles in the right triangle is 45 degrees and 45 degrees.