Question

In a parallelogram ABCD, P and Q are mid-points of sides DA and DC respectively. If $\angle DAC={30}^{\circ }$, then find the values of x and y?
[2 MARKS]

Answer 1

Concept : 1 Mark
Calculation : 1 Mark

In $\Delta ADC$, P and Q are mid points of line DA and DC respectively.

So $PQ\parallel AC$

$\angle DPQ=\angle PAC={30}^{\circ }$ (corresponding)

$\angle y={30}^{\circ }$

In $\Delta PDQ$ , by the angle sum property, we have,

$y+{120}^{\circ }+\angle DQP={180}^{\circ }$

$\Rightarrow {30}^{\circ }+{120}^{\circ }+\angle DQP={180}^{\circ }$

$\Rightarrow DQP={30}^{\circ }$

$\Rightarrow \angle x={180}^{\circ }-\angle DQP={180}^{\circ }-{30}^{\circ }={150}^{\circ }$