Question

Consider the following parallelograms. Find the values of the unknowns $x,y,z$

Answer 1

(i) $x+100=180$ [Adjacent angles]
$x=80$
$z=x={80}^{\circ }$ [opposite angles are equal]
$y={100}^{\circ }$

(ii) $50+y=180$
$y={130}^{\circ }$
$x=y={130}^{\circ }$ and $z=x={130}^{\circ }$ (corresponding angles)

(iii) $x={90}^{\circ }$ (vertically opposite angles)
$x+y+30={180}^{\circ }$
$y=180-120={60}^{\circ }$
$z=y={60}^{\circ }$ (Alternate angles)

(iv) $z=80,y=80$ (Opposite angles)
$x+y={180}^{\circ },x=180-80\Rightarrow x={100}^{\circ }$

(v) $y={112}^{\circ }$ (opposite angles)
$x+y+40={180}^{\circ }$ (Angle sum property)
$x=180-152$
$x={28}^{\circ }$
$z=x={28}^{\circ }$ (Alternate angles)