Question

Find the value of x in the following figure:

• A. ${106}^{\circ }$
• B. ${56}^{\circ }$
• C. ${26}^{\circ }$
• D. ${46}^{\circ }$

Answer 1

The correct option is C ${26}^{\circ }$

Angle sum property of a triangle tells sum of interior angles of a triangle is 180°.

$\text{In}\Delta ABC$,

$\angle ACB+\angle CBA+\angle BAC={180}^{\circ }$

$\Rightarrow \angle ACB+{35}^{\circ }+{39}^{\circ }={180}^{\circ }$

$\Rightarrow \angle ACB={180}^{\circ }-({35}^{\circ }+{39}^{\circ })$

$={180}^{\circ }-{74}^{\circ }$

$={106}^{\circ }$

Here, AE and BD interesect at C.

$\Rightarrow \angle DCE=\angle ACB={106}^{\circ }$
[∵ vertical angles]

In $\Delta DEC$,
$\angle DCE+\angle CED+\angle EDC={180}^{\circ }$
[Angle sum property]

$\Rightarrow {106}^{\circ }+{48}^{\circ }+x={180}^{\circ }$

$\Rightarrow x={180}^{\circ }-({106}^{\circ }+{48}^{\circ })$
$={26}^{\circ }$

So, value of x is 26°.