Question

In the following figure ABCD and PQRS are parallelograms. Find the measure of x. (2 marks)

Answer 1

In the parallelogram ABCD,

$\angle ABC$ + $\angle BAD$ = 180${}^{\circ }$
[sum of adjacent angles of a parallelogram is 180${}^{\circ }$]

$\angle ABC$ = 180${}^{\circ }$ − 120${}^{\circ }$ = 60${}^{\circ }$ (1 mark)

Similarly, in parallelogram PQRS

$\angle PQR$ = $\angle PSR$ = 70${}^{\circ }$
[Opposite angles of a parallelogram are equal]

In the triangle:

$x$ + $\angle PSR$ +$\angle ABC$ = 180${}^{\circ }$ [Angle sum property]
$\Rightarrow$$x$ = 180${}^{\circ }$ − (70${}^{\circ }$ + 60${}^{\circ }$)
$\Rightarrow$$x$ =50${}^{\circ }$ (1 mark)