Question

In AOPQ, OQ is extended through point Q to point R, mZPQR = (4x – 10°), mZOPQ = (x +9)°, and mZQOP = (x – 5)'. Find measure?

Answer 1

For solving such problems, we use the fact that the sum of angles in a triangle equals 180 degrees. Substitute the expressions for angles given as expressions of x into this equation and solve for x. Then substitute back x into the expressions to find the measures of each angle.

Step-by-step explanation:

Given the geometric problem with angles, we can first understand what each term means. In triangle AOPQ, line OQ is

extended through point Q to point R. We know that mZPQR = (4x – 10°), mZOPQ = (x +9)°, and mZQOP = (x – 5)°. This defines the measures of the respective angles. To solve for x, we can use the principle that the sum of angles in a triangle equals 180 degrees - implying that mZOPQ + mZQOP + mZPQR = 180. Substitute the given values and solve for x to get the values of the angles. Once you have found x, substitute it back into the expressions for each

measure

to get their values. As the figure is not provided, a more specific solution cannot be given.

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