Answer:
m∠K = 43°
m∠N = 75°
m∠B = 62°
Explanation:
Pre-Solving
We are given ΔKNB.
We know that m∠K = 2x + 17 degrees, m∠N = 5x + 10 degrees, and m∠B = 4x+10 degrees.
We want to find the measure of each angle.
Recall that the measures of all angles in a triangle equals 180°.
This means m∠K + m∠N + m∠B = 180°.
Or, 2x + 17 + 5x + 10 + 4x + 10 = 180.
Solving
We can evaluate the equation we just made: 2x + 17 + 5x + 10 + 4x + 10 = 180
Combine like terms.
11x + 37 = 180
Subtract 37 from both sides.
11x = 143
Divide both sides by 11
x = 13
We found the value of x, but now we need to find the measures of the angles:
Substitute 13 as x.
For angle K, that means:
m∠K = 2(13) + 17 = 43°
For angle N, that means:
m∠N = 5(13) + 10 = 75°
For angle B, that means:
m∠B = 4(13) + 10 = 62°