Question

Using the information, given in each of the following figures, find the valuesof a.
[ Given : $CE=AC$]

• A. ${136}^o$
• B. ${124}^o$
• C. ${110}^o$
• D. none of the above

Answer 1

The correct option is B ${124}^o$

In $△ACE$,
Given, AC = EC
$\angle AEC=\angle EAC=x$ (Isosceles triangle property)
Sum of angles of triangle = 180
$\angle AEC+\angle EAC+\angle ACE=180$
$x+x+68=180$
$x={56}^{\circ }$
Now, $a=\angle EAC+\angle ECA$ (Exterior angle property)
$a=56+68$
$a={124}^{\circ }$
Given, $BA\parallel CD$
$\angle BAC+\angle DCA=180$
$\angle BAE+\angle EAC+\angle ACB+\angle BCD=180$
$14+56+68+b=180$
$b=180-138$
$b={42}^{\circ }$