Answer:
m∠N = 41°
Explanation:
Here,
In △MNO, m∠M = (6x + 1°) ...(1)
m∠N = (3x - 10°) ...(2)
m∠0 = (x + 19°) ...(3)
Here, We know that the sum of all angles of a triangle is 180°
Then,
(6x + 1°) + (3x - 10°) + (x + 19°) = 180°
6x + 1° + 3x - 10° + x + 19° = 180°
6x + 3x + x + 1° - 10° + 19° = 180°
10x + 10° = 180°
10x = 180° - 10°
10x = 170°
x = 170° ÷ 10°
x = 17°
Now, put the value of x in (1), (2) and (3)
m∠M = (6x + 1°)
= (6(17) + 1°)
= (102° + 1°)
m∠M = 103°
m∠N = (3x - 10°)
= (3(17) - 10°)
= (51° - 10°)
m∠N = 41°
m∠0 = (x + 19°)
= (17 + 19°)
m∠0 = 36°
Thus, The m∠N = 41°
FOR VERIFICATION ONLY:
(6x + 1°) + (3x - 10°) + (x + 19°) = 180°
(6(17) + 1°) + (3(17) - 10°) + (17 + 19°) = 180°
103° + 41° + 36° = 180°
180° = 180°
Hence, L.H.S = R.H.S
-TheUnknownScientist