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The difference of two complementary angles is 11 degrees. Find the measures of the angles (in degrees).

User BowPark
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Answer:

Explanation:

Let's begin by using the definition of complementary angles: two angles are complementary if their sum is 90 degrees. We can express the two angles as x and y, and we know that:

x + y = 90 (equation 1)

We also know that the difference between the angles is 11 degrees, which we can express as:

x - y = 11 (equation 2)

We now have two equations with two unknowns, so we can solve for x and y by adding equation 1 and equation 2, which eliminates the y term:

(x + y) + (x - y) = 90 + 11

2x = 101

x = 50.5

Now we can use equation 1 to solve for y:

x + y = 90

50.5 + y = 90

y = 39.5

Therefore, the measures of the two complementary angles are 50.5 degrees and 39.5 degrees.

User Kenziiee Flavius
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