m∠N = 41°
Explanation:
m∠M = (6x + 1)°
m∠N = (3x – 10)°
m∠O = (x + 19)°
Triangle MNO:
m∠M + m∠N + m∠O = 180 degrees (sum of angles in a triangle)
(6x + 1)° + (3x – 10)° + (x + 19)° = 180°
6x + 1 + 3x - 10 + x + 19 = 180
collect like terms:
6x + 3x + x + 1 - 10 + 19 = 180
10x + 10 = 180
10x = 180 - 10
10x = 170
divide both sides by 10:
10x/10 = 170/10
x = 17
m∠N = (3x – 10)° = 3(17) - 10 = 51 - 10
m∠N = 41°
