Final answer:
To find the value of x in triangle OPQ, we use the fact that the sum of interior angles in a triangle is always 180 degrees. Upon setting up and solving the equation (2x - 5) + (3x - 8) + (10x - 17) = 180, we determine that x equals 14.
Step-by-step explanation:
In triangle OPQ, we need to find the value of x given the angle measures expressed in terms of x. To solve this, we can use the fact that the sum of the interior angles in any triangle equals 180 degrees. We can set up an equation based on this fact:
m∠O + m∠P + m∠Q = 180°
By substituting the given expressions:
(2x - 5)° + (3x - 8)° + (10x - 17)° = 180°
Combine like terms:
15x - 30 = 180
Adding 30 to both sides gives us:
15x = 210
Divide both sides by 15 to find the value of x:
x = 14
This gives us the value for x required for the measures of angles in ΔOPQ.