Question

Triangles $ABC$ and $CDE$ are isosceles triangles, $ACEF$ is a straight line. Find the value of $y$.

• A. ${52}^{\circ }$
• B. ${58}^{\circ }$
• C. ${68}^{\circ }$
• D. ${76}^{\circ }$

Answer 1

The correct option is D ${76}^{\circ }$

$\Delta$ABC and $\Delta$DCE is an isosceles triangle

$\angle DEC+\angle DEF=180$

$\angle DEC=180-124$

$\angle DEC={56}^o$

$\angle DCE=\angle DEC$ (since, $\Delta DCE$ is an isosceles $\Delta$)

$\angle BCA+\angle BCD+\angle DCE={180}^o$

$\angle BCA+72+{56}^o={180}^o$

$\angle BCA={52}^o$

In $\Delta$ABC

$\angle BAC=\angle BCA$ (isosceles $\Delta$)

$\angle y+\angle BAC+\angle BCA={180}^o$

$\angle y+52+{52}^o={180}^o$

$\angle y={76}^o$.