Question

What is the measure of YXJ angle

Answer 1

`\mathrm{m\angle YZJ=(1)/(2)(arc\ YZX)}[\mathrm{The\ measure\ of\ an\ inscribed\ angle\ is\ half\ of\ it's}\\\mathrm{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ intercepted\ arc.]}\\\mathrm{or,\ m\angle YZJ=(1)/(2)(94^o+62^o)}\ \ \ \\\mathrm{or,\ m\angle YZJ=78^o}\\`

`\mathrm{Now,}\\\mathrm{ m\angle YXJ+m\angle YZJ=180^o\ \ \ [Opposite\ angles\ of\ cyclic\ quadrilateral\ are}\\\mathrm{\ \ \ \ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ supplementary.]}\\\mathrm{or,\ m\angle YXJ+78^o=180^o}\\\therefore\ \mathrm{m\angle YXJ=102^o}`