First find \(x\). Then find m(\(\angle{ZYQ})\) and m(\(\angle{PYQ})\)

Explanation

1. To find x, use the vertical angles rule where ∠ZYQ and ∠XYP are vertical, then their measures are the same
   • 4x + 15^o = 7x - 60^o
   • 3x = 75^o
   • x = 25^o
2. Substitute x in the measure of angle ∠ZYQ,
   • m(∠ZYQ)= 7x - 60^o = 7 * 25^o - 60^o = 115
3. ∠ZYQ and ∠PYQ are supplementary, then
   • m(∠PYQ) = 180^o - 115^o = 65^o