One of two complementary angles has a measure of 6º greater than the other. What is the measures of the larger angle? What is the measure of the smaller angle?
Two complementary angles have to add up to 180
so
x + x+6 = 180
take over
The sum of 2 complimentary angles = 90o.
To solve this problem, we can set up an equation based on the information given.
Let x be the measure of the smaller angle.
According to the given information, the measure of the larger angle is 6º greater than the smaller angle. Therefore, the measure of the larger angle is x + 6.
Since the sum of the measures of complementary angles is 90º, we can set up the equation:
x + (x + 6) = 90
Now, we can solve this equation to find the value of x.
Combining like terms, we have:
2x + 6 = 90
Next, let's isolate the variable by subtracting 6 from both sides:
2x = 84
Finally, we can solve for x by dividing both sides by 2:
x = 42
Therefore, the measure of the smaller angle is 42º.
To find the measure of the larger angle, we can substitute the value of x back into x + 6:
42 + 6 = 48
Therefore, the measure of the larger angle is 48º.
So, the measures of the larger angle and the smaller angle are 48º and 42º, respectively.