Answer:
m∠MNO = 26°
Explanation:
In the figure attached,
Angle MNO is an external angle of triangle LMN,
m∠NLM = (x + 1)°
m∠LMN = (x + 15)°
m∠MNO = (4x + 6)°
Therefore, by theorem of exterior angle of a triangle,
m∠MNO = m∠NLM + m∠LMN
(4x + 6)° = (x + 1)° + (x + 15)°
4x + 6 = 2x + 16
4x - 2x = 16 - 6
2x = 10
x = 5
Now m∠MNO = (4x + 6)°
= (4 × 5) + 6
= 26°
Therefore, measure of angle MNO is 26°