If /_1 and /_2 are complementary angles, and m /_1=5x-9 and m/_2=4x, find the measure of the two angles.
A+B = 90
A = 5x-9
B = 4x
A+B = 9x-9 = 90
9x = 99
x = 11
A = 55-9 = 46
B = 4(11) =44
To find the measure of the two angles, we can set up an equation based on the given information.
We know that complementary angles add up to 90 degrees. So we can write the equation:
m /_1 + m /_2 = 90
Substituting the given values, we have:
(5x - 9) + (4x) = 90
Now we can solve for x by combining like terms:
9x - 9 = 90
Add 9 to both sides:
9x = 99
Divide both sides by 9:
x = 11
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures.
m /_1 = 5x - 9
Substituting x = 11:
m /_1 = 5(11) - 9 = 55 - 9 = 46.
Therefore, the measure of angle /_1 is 46 degrees.
m /_2 = 4x
Substituting x = 11:
m /_2 = 4(11) = 44.
Therefore, the measure of angle /_2 is 44 degrees.