Get it on Google Play
4. In figure, \(\angle{ABC}\) = \(69^\circ\), \(\angle{ACB}\) = \(31^\circ\). Find \(\angle{BDC}\).
image
Answer :

As we know that, the angles in the same segment are equal.
We get, \(\angle{BDC}\) = \(\angle{BAC}\) ...(i)
Now, in \(\triangle{ABC}\),
\(\angle{BAC}\) + \(\angle{ABC}\) + \(\angle{ACB}\) = \(180^\circ\)
i.e., \(\angle{BAC}\) + \(69^\circ\) + \(31^\circ\) = \(180^\circ\)
i.e., \(\angle{ABC}\) + \(100^\circ\) = \(180^\circ\)
i.e., \(\angle{ABC}\) = \(180^\circ\) - \(100^\circ\)
So, \(\angle{BAC}\) = \(80^\circ\)
Therefore, \(\angle{BDC}\) = \(80^\circ\) ...(from (i))