Question

2 find ( moverarc{pr} )

( -7 + 6x )

( -2 + 11x )

Explanation:

Step1: Assume the triangle is isosceles (since it's in a circle, maybe inscribed angles or arcs, but here probably the two angles at Q? Wait, no, the arcs: Wait, the arc PR is -2 + 11x, and the angle at Q is -7 + 6x? Wait, maybe the inscribed angle theorem: the measure of an inscribed angle is half the measure of its intercepted arc. Wait, but maybe the triangle PQR is isosceles? Wait, no, maybe the arc PR and the angle at Q: Wait, perhaps the angle at Q is an inscribed angle intercepting arc PR? Wait, no, inscribed angle intercepts arc PR, so angle Q would be half of arc PR? Wait, no, maybe the two arcs: Wait, maybe the problem is that the angle at Q is equal to half the arc PR? Wait, no, maybe the triangle is isosceles, so the two angles are equal? Wait, no, the expressions are -7 + 6x (angle at Q) and the arc PR is -2 + 11x. Wait, maybe the inscribed angle theorem: the measure of an inscribed angle is half the measure of its intercepted arc. So angle Q intercepts arc PR, so angle Q = 1/2 arc PR. So:

$-7 + 6x = \frac{1}{2}(-2 + 11x)$

Step2: Solve for x. Multiply both sides by 2:

$2(-7 + 6x) = -2 + 11x$

$-14 + 12x = -2 + 11x$

Subtract 11x from both sides:

$-14 + x = -2$

Add 14 to both sides:

$x = 12$

Step3: Substitute x = 12 into the arc PR formula: -2 + 11x

$-2 + 11(12) = -2 + 132 = 130$

Answer:

130