Question

In the diagram below, what are the values of the pronumerals? Show working

Answer 1

`\mathrm{The\ given\ figure\ is\ relabeled\ as\ follows:}\\\mathrm{From\ the\ figure,}\\\mathrm{OA=OB\ \ \ [Radii\ of\ same\ circle\ is\ equal.]}\\\mathrm{\angle OAB=\angle OAC=}a^o\ \ \ [\mathrm{OA=OB,\ base\ angles\ of\ isosceles\ triangle\ OAB.}]\\`

`\mathrm{Now},\\\ \mathrm{\angle OAB+\angle OBA+70^o=180^o\ \ \ [Sum\ of\ interior\ angles\ of\ triangle\ is\ 180^o.]}\\\mathrm{or,\ }a^o+a^o+70^o=180^o\\\mathrm{or,\ }2a^o=110^o\\\mathrm{or,\ }a^o=55^o`

`\mathrm{Finally,}\\\mathrm{\angle BCA=(1)/(2)\angle BOA\ \ \ [Inscribed\ angle\ is\ half\ of\ the\ central\ angle\ on \same\ arc.]}\\\\\mathrm{or,\ }b^o=(1)/(2)* 70^o\\\\\mathrm{or,\ }b^o=35^o`