Question

Question 128

In $\Delta ABC$, $DE\parallel BC$ (figure). Find the values of x, y and z.

Answer 1

In $\Delta ABC,\angle A+\angle B+\angle C={180}^{\circ }$ [sum of all angles of a triangle is ${180}^{\circ }$]
$\Rightarrow z+{30}^{\circ }+{40}^{\circ }={180}^{\circ }\Rightarrow z+{70}^{\circ }={180}^{\circ }\Rightarrow z={180}^{\circ }-{70}^{\circ }={110}^{\circ }\because DE\parallel BC$
Now, $\angle ADE=\angle ABC$ [$\because$ corresponding angles are equal]
$\Rightarrow \angle x={30}^{\circ }$ and $\angle AED=\angle ACB$

[$\because$ corresponding angles are equal]
$\Rightarrow \angle y={40}^{\circ }$