Question
Find the unknown marked angles in the given figure:
✓
Answer
$\angle B+\angle A B C=180^{\circ} \ldots$ (Linear pair)
$
\begin{aligned}
& \angle B+140^{\circ}=180^{\circ} \\
& \angle B=180^{\circ}-140^{\circ} \\
& \angle B=40^{\circ}
\end{aligned}
$
Exterior angle $=$ sum of its interior opposite angles
$
\begin{aligned}
& 2 m+40^{\circ}=4 m \\
& 2 m-4 m=-40^{\circ} \\
& -2 m=-40^{\circ}
\end{aligned}
$
$
\begin{aligned}
& 2 m=40^{\circ} \\
& m=\frac{40}{2} \\
& m =20^{\circ}
\end{aligned}
$
$
\begin{aligned}
& \angle A =2 m =2 \times 20^{\circ}=40^{\circ} \\
& \angle B=40^{\circ} \\
& \angle D =4 m =4 \times 20^{\circ}=80^{\circ}
\end{aligned}
$
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