Question

In the figure, AB = AC and BC is procured to D,
if CDE = 20° and BAC = 80°, then find the
angle of CED.​

Answer 1

Answer:

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Given :

\begin{gathered}AB=AC\\\\\angle BAC=80^\circ\end{gathered}AB=AC∠BAC=80∘

To find : \angle ABC=?∠ABC=?

Solution :

In ΔABC, it is an isosceles triangle,

So, ∠ ABC = ∠ACB = x

According to the sum of angles of triangle :

\begin{gathered}\angle A+\angle B+\angle C=180^\circ\\\\80^\circ+x+x=180^\circ\\\\2x=180-80\\\\2x=100\\\\x=\dfrac{100}{2}\\\\x=50^\circ\end{gathered}∠A+∠B+∠C=180∘80∘+x+x=180∘2x=180−802x=100x=2100x=50∘

Hence, the measure of \angle ABC=50^\circ∠ABC=50∘.