Final answer:
To find the measure of angle R in triangle APQR, the equation formed by the sum of the angles equaling 180 degrees is solved for x and then substituted back into the expression for m∠R, resulting in a measure of 17 degrees for angle R.
Step-by-step explanation:
The student has been given a problem involving triangle APQR, with the measures of the angles provided as algebraic expressions in terms of a variable x. The measure of angle P is (4x - 14)°, the measure of angle Q is (5x + 6)°, and the measure of angle R is (x - 2)°. The sum of the angles in any triangle is always 180 degrees, so we can set up and solve the following equation:
4x - 14 + 5x + 6 + x - 2 = 180
Combining like terms, we get:
10x - 10 = 180
Adding 10 to both sides gives us:
10x = 190
Dividing both sides by 10 gives us:
x = 19
Now we can find the measure of angle R by substituting the value of x into the expression for m∠R:
m∠R = x - 2 = 19 - 2 = 17 degrees