Final answer:
The value of x in triangle OPQ is 14°.
Step-by-step explanation:
In triangle OPQ, we have angles: ∠O = (2x-5)°, ∠P = (3x-8)°, and ∠Q = (10x-17)°.
The sum of angles in a triangle is always 180°, so we can set up an equation:
(2x-5) + (3x-8) + (10x-17) = 180°
Simplifying the equation, we get:
(2x + 3x + 10x) - (5 + 8 + 17) = 180°
Combining like terms:
15x - 30 = 180°
Adding 30 to both sides:
15x = 210°
Dividing both sides by 15:
x = 14°
So, the value of x is 14°.