Final answer:
The value of x in ∆MNO, where m∠M = (2x+10)°, m∠N = (9x+10)°, and m∠O = (x+16)°, is found by setting up and solving the equation (2x + 10) + (9x + 10) + (x + 16) = 180. After simplification, x is found to be 12.
Step-by-step explanation:
In ∆MNO, the sum of the angles must equal 180 degrees because it is a triangle. Given that m∠M = (2x+10)°, m∠N = (9x+10)°, and m∠O = (x+16)°, we can set up the following equation to find the value of x:
(2x + 10) + (9x + 10) + (x + 16) = 180
Simplifying the equation, we get:
12x + 36 = 180
Subtracting 36 from both sides, we get:
12x = 144
Dividing both sides by 12, we find that x = 12.