In parallelogram $ABCD$, the bisectors of $\angle A$ and $\angle B$ meet at $P$. Then $\angle APB$ equals:

In parallelogram $ABCD$, the bisectors of $\angle A$ and $\angle B$ meet at $P$. Then $\angle APB$ equals:
  1. $60^{\circ}$
  2. $90^{\circ}$
  3. $120^{\circ}$
  4. Depends on the parallelogram

Solution

Adjacent angles of a parallelogram are supplementary, so $\angle A + \angle B = 180^{\circ}$. In $\triangle APB$: $\angle APB = 180 - (\angle A/2 + \angle B/2) = 180 - 90 = 90^{\circ}$.

Asked in: IMO

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