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
   • 2x + 35^o = 6x - 5^o
   • 4x = 40^o
   • x = 10^o
2. Substitute x in the measure of angle ∠ZYQ,
   • m(∠ZYQ)= 2x + 35^o = 2 * 10^o + 35^o = 55
3. ∠ZYQ and ∠PYQ are supplementary, then
   • m(∠PYQ) = 180^o - 55^o = 125^o