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two angles are complementary. one angle is 4 less than 7 times the other. find the measure of each angle.​

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Final answer:

Two complementary angles can be found by solving a system of equations. One angle is 82.25 degrees and the other angle is 11.75 degrees.

Step-by-step explanation:

Let's call one angle x and the other angle y.

We know that the two angles are complementary, which means they add up to 90 degrees.

We also know that one angle is 4 less than 7 times the other.

So, we can write the following equation: x + y = 90 and x = (7y) - 4.

Solving these two equations simultaneously, we can find the values of x and y. Substituting x in the first equation, we have (7y) - 4 + y = 90.

Combining like terms, we get:

8y - 4 = 90

Adding 4 to both sides, we get:

8y = 94

Dividing both sides by 8, we get:

y = 11.75

Substituting the value of y back into the second equation, we get:

x = (7 * 11.75) - 4 = 82.25

So, the measure of one angle is 82.25 degrees and the measure of the other angle is 11.75 degrees.

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