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The measure of one of the small angles of a right triangle is 18 more than 3 times the measure of the other small angle. Find the measure of both angles (in degrees).

User Neel Kamal
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Answer:

Therefore, the measure of the other small angle is 72 degrees.

Explanation:

Let's call the measure of one of the small angles "x" and the measure of the other small angle "y".

We know that the two small angles of a right triangle are complementary, which means their sum is 90 degrees. So we have:

x + y = 90

We also know that one of the small angles is 18 more than 3 times the other. We can express this as:

x = 3y + 18

Now we can substitute the expression for x into the first equation:

x + y = 90

(3y + 18) + y = 90

Combining like terms, we get:

4y + 18 = 90

Subtracting 18 from both sides, we get:

4y = 72

Dividing both sides by 4, we get:

y = 18

So one of the small angles is 18 degrees.

To find the other small angle, we can use the expression we found for x in terms of y:

x = 3y + 18

Substituting y = 18, we get:

x = 3(18) + 18 = 72

Therefore, the measure of the other small angle is 72 degrees.

User Leo Dabus
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