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.