[tex]\angle MYZ\ \text{and}\ \angle XYZ\ \text{are supplementary angles.}\\\text{The sum of their measures is 180}^o.\\\\\text{We have}\ m\angle MYZ=115^o.\ \text{Therefore:}\\\\m\angle XYZ=180^o-115^o=65^o.\\\\\text{We know: The sum of the measures of the angles in the triangle is 180}^o.\\\text{Therefore we have the equation:}\\\\65^o+(4k+5)^o+(6k+10)^o=180^o\\\\65+4k+5+6k+10=180\\\\(4k+6k)+(65+5+10)=180\\\\10k+80=180\qquad\text{subtract 80 from both sides}\\\\10k=100\qquad\text{divide both sides by 10}\\\\\boxed{k=10}[/tex]
