Question

In the figure, PQ|| AB and PR|| BC. If $\angle QPR={102}^0$, Determine $\angle ABC$. Give reasons.

Answer 1

In the figure, PQ||AB and PR ||BC $\angle QPR={102}^0$ Produce BA to meet PR at D
$\because PQ||ABorDB$
$\therefore \angle QPR=\angle ADR$ (Corresponding angles)
$\therefore \angle ADR={102}^{0}or\angle BDR={102}^0$
$\because PR||BC$
$\therefore \angle BDR+\angle DBC={180}^0$
(Sum of co-interior angles)
$\Rightarrow {102}^0+\angle DBC={180}^0$
$\Rightarrow \angle DBC={180}^0-{102}^0={78}^0$
$\Rightarrow ABC={78}^0$