Answer:
This equation is true, so our solution is correct. Therefore, the measure of the larger angle is 74 degrees.
Explanation:
Let's call the measure of the smaller angle "x".
We know that the two angles are complementary, which means they add up to 90 degrees. So the larger angle is 90 - x degrees.
We also know that the measure of the larger angle is ten more than four times the measure of the smaller angle. We can express this in an equation:
90 - x = 4x + 10
Simplifying this equation, we get:
90 = 5x + 10
Subtracting 10 from both sides, we get:
80 = 5x
Dividing both sides by 5, we get:
x = 16
So the measure of the smaller angle is 16 degrees.
To find the measure of the larger angle, we can use the equation we set up earlier:
90 - x = 4x + 10
Substituting x = 16, we get:
90 - 16 = 4(16) + 10
Simplifying, we get:
74 = 74
This equation is true, so our solution is correct. Therefore, the measure of the larger angle is 74 degrees.