Final answer:
In triangle OPQ, the value of x that satisfies the given angles is found by setting the sum of angles equal to 180 degrees and solving the resulting equation, which gives x = 14.
Step-by-step explanation:
To find the value of x in triangle OPQ with angles m∠O = (2x-5)°, m∠P = (3x-8)°, and m∠Q = (10x - 17)°, we can use the fact that the sum of angles in any triangle is always 180 degrees.
Therefore, we can set up an equation by adding all three angles and setting their sum equal to 180°: (2x-5) + (3x-8) + (10x - 17) = 180.
Simplifying this equation,
- 2x + 3x + 10x = 15x
- -5 - 8 - 17 = -30
- 15x - 30 = 180
Adding 30 to both sides gives us 15x = 210, and dividing both sides by 15 gives us x = 14.
This is the value of x that satisfies all three given angles of triangle OPQ.