Question

Using information given in the adjacent figure, find the value of $x^{\circ }$ .

Answer 1

In the given figure, $ABCD$ is a quadrilateral.

Let us try to divide it into two triangles.

Join $AC$ and produce it to $E$.

Let $\angle DAE=p^{\circ },\angle BAE=q^{\circ },\angle DCE=z^{\circ }$ and $\angle ECB=t^{\circ }$.

So, $p^{\circ }+q^{\circ }={46}^{\circ }......\left(1\right)$

Since the exterior angle of a triangle is equal to the sum of the interior opposite angles, we have,

$z^{\circ }=p^{\circ }+{26}^{\circ }......\left(2\right)$

and, $t^{\circ }=q^{\circ }+{38}^{\circ }......\left(3\right)$

Now,

$x^{\circ }=z^{\circ }+t^{\circ }$

$=p^{\circ }+{26}^{\circ }+q^{\circ }+{38}^{\circ }$

$=(p^{\circ }+q^{\circ })+(26+38{)}^{\circ }$

$={46}^{\circ }+{64}^{\circ }$

$={110}^{\circ }$

Hence, the value of $x^{\circ }$ is ${110}^{\circ }$ .