The value of x is 8 degrees and the measure of RQ is 131 degrees.
To find the value of x in the given triangle, we can use the following equation:
The sum of the angles in a triangle = 180 degrees
Therefore, we have:
(9x + 17) + (6x - 12) + (5x + 15) = 180 degrees
Combining like terms, we get:
20x + 20 = 180 degrees
Subtracting 20 from both sides, we get:
20x = 160 degrees
Dividing both sides by 20, we get:
x = 8 degrees
Therefore, the value of x is **8 degrees.
To find the measure of RQ, we can use the following equation:
Exterior angle of a triangle = Sum of the two remote interior angles
Therefore, we have:
(5x + 15) + (9x + 17) = RQ
Substituting x with its value, we get:
RQ = (5 * 8 + 15) + (9 * 8 + 17)
Evaluating the expression, we get:
RQ = 40 + 91
Therefore, the measure of RQ is 131 degrees.
In summary, the value of x is 8 degrees and the measure of RQ is 131 degrees.