Question

If $\angle A={100}^{\circ }$, AB = AC, CD bisects $\angle ACB$ and BD bisects $\angle ABC$. The values of x and y are

• A. ${15}^{\circ }and{70}^{\circ }$
• B. ${20}^{\circ }and{140}^{\circ }$
• C. ${10}^{\circ }and{160}^{\circ }$
• D. ${20}^{\circ }and{125}^{\circ }$

Answer 1

The correct option is B ${20}^{\circ }and{140}^{\circ }$

$SinceAB=AC$
$\therefore \angle ABC=\angle ACB$
$\therefore 2x+2x+{100}^{\circ }={180}^{\circ }\Rightarrow 4x={80}^{\circ }$
$\angle x={20}^{\circ }$
$In\Delta DBC,$
$x+x+y={180}^{\circ }\Rightarrow {40}^{\circ }+y={180}^{\circ }-{40}^{\circ }={140}^{\circ }.$