If angle <a and <b are complementary but <a is four times as large as <b, find the measurement of a.
a+b = 90
a = 4 b
5 b = 90
b = 18
a = 4*18 = 72
To find the measurement of angle a, we need to use the information given.
Let's assume the measurement of angle b is x degrees.
Since angle a is four times as large as angle b, we can express angle a as 4x degrees.
Since angle a and angle b are complementary, the sum of their measures is 90 degrees.
So we can write the equation:
4x + x = 90
Combining like terms, we get:
5x = 90
To isolate x, we divide both sides of the equation by 5:
x = 90/5 = 18
Therefore, angle b measures 18 degrees.
To find the measurement of angle a, we substitute this value back into the equation:
a = 4x = 4 * 18 = 72
Therefore, angle a measures 72 degrees.