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Angle k and angle l form complimentary angles . If m angle k = (3x+3)° and m angle l= (10x-4)°, find the measure of each angle.

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Answer: K is 24 degrees, L is 66 degrees.

Explanation:

Complementary angles are two angles whose measures add up to 90 degrees. In this case, angle K (m∠K) and angle L (m∠L) are complementary, so we have:

m∠K + m∠L = 90 degrees

Now, let's substitute the expressions for m∠K and m∠L from the given information:

(3x + 3)° + (10x - 4)° = 90°

Now, combine like terms and solve for x:

3x + 3 + 10x - 4 = 90

13x - 1 = 90

Add 1 to both sides:

13x = 91

Now, divide by 13 to solve for x:

x = 91 / 13

x = 7

Now that we have found the value of x, we can find the measures of angles K and L:

m∠K = 3x + 3

m∠K = 3(7) + 3

m∠K = 21 + 3

m∠K = 24 degrees

m∠L = 10x - 4

m∠L = 10(7) - 4

m∠L = 70 - 4

m∠L = 66 degrees

So, the measure of angle K is 24 degrees, and the measure of angle L is 66 degrees.

User Evgnomon
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