Question

In Fig., $ \angle ABC=69°$,,$ \angle ACB=31°$, find $ \angle BDC$

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Answer 1

Find the given angle

We need to find, $\angle BDC$

Given, $\angle ABC=69°$ and $\angle ACB=31°$

So,

In $∆ABC$

$$\begin{gathered} \Rightarrow \angle A+\angle B+\angle C=180°\left[\mathrm{Angle}\mathrm{sum}\mathrm{property}\mathrm{of}\mathrm{triangle}\right] \\ \Rightarrow \angle A+69°+31°=180° \\ \Rightarrow \angle A+100°=180° \\ \Rightarrow \angle A=80° \end{gathered}$$

$\angle A$ and $\angle D$ lie on same line segment

Therefore

$$\begin{gathered} \Rightarrow \angle D=\angle A \\ \Rightarrow \angle D=80° \end{gathered}$$

Hence $\angle BDC=80°$