Question

K and L are complementary angles. If mK = (3x + 3)º and

mL = (10x – 4)º, find the measure of each angle.

Answer 1

∠ K = 24° , ∠ L = 66°

Step-by-step explanation:

complementary angles , sum to 90°

sum the 2 angles, equate to 90 and solve for x

3x + 3 + 10x - 4 = 90 ( simplify left side )

13x - 1 = 90 ( add 1 to both sides )

13x = 91 ( divide both sides by 13 )

x = 7

Then

∠ K = 3x + 3 = 3(7) + 3 = 21 + 3 = 24°

∠ L = 10x - 4 = 10(7) - 4 = 70 - 4 = 66°

Answer 2

To find the measures of complementary angles K and L with given expressions, we set up an equation based on the definition of complementary angles, solve for x, and substitute back to find that angle K is 24 degrees and angle L is 66 degrees.

Step-by-step explanation:

K and L are complementary angles, which means the sum of their measures is 90 degrees. The measure of angle K is mK = (3x + 3)° and the measure of angle L is mL = (10x – 4)°. To find the measures of these angles, we set up the equation (3x + 3) + (10x – 4) = 90 and solve for x.

1. Combine like terms: 13x - 1 = 90.
2. Add 1 to both sides: 13x = 91.
3. Divide by 13: x = 7.
4. Substitute x back into the expressions for mK and mL: mK = (3(7) + 3) = 24° and mL = (10(7) - 4) = 66°.

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