Question

Given ABCD is a parallelogram, find the measure of $x-2y+z$ in degrees form the following figure.

Answer 1

ABCD is a $\parallel gm$ , therefore

$x={110}^{\circ }$

In $△ADC$

${110}^{\circ }+{40}^{\circ }+y={180}^{\circ }$

$y={180}^{\circ }-{150}^{\circ }={30}^{\circ }$

$CD\parallel AB$ , $\therefore$ $y=z={30}^{\circ }$ [Alternate]

Now, $x-2y+z={110}^{\circ }-2\ast {30}^{\circ }+{30}^{\circ }$

$={110}^{\circ }-{60}^{\circ }+{30}^{\circ }$

$={80}^{\circ }$