Question

In the figure, ABC is isosceles triangle whose side AC is produced E. Through C, CD is drawn parallel to BA. The value of x is

• A. ${52}^{\circ }$
• B. ${76}^{\circ }$
• C. ${156}^{\circ }$
• D. ${104}^{\circ }$

Answer 1

The correct option is D

${104}^{\circ }$

$In\Delta ABC,AB=AC$

$\text{AC is produced to E}$

$CD||BA\text{is drawn}$

$\angle ABC={52}^{\circ }$

$\therefore \angle ACB={52}^{\circ }(\because AB=AC)$

$\therefore \angle BAC={180}^{\circ }-({52}^{\circ }+{52}^{\circ })$$={180}^{\circ }-{104}^{\circ }={76}^{\circ }$

$\because AB||CD$

$\therefore \angle ACD=\angle BAC\text{(Alternate angles)}$

$={76}^{\circ }$

$\angle x+\angle ACD={180}^{\circ }\Rightarrow x+{76}^{\circ }={180}^{\circ }$

$\therefore x={180}^{\circ }-{76}^{\circ }={104}^{\circ }$