Question:
In $\triangle DEF$ shown, points A, B, and C are taken on DE, DF, and EF respectively such that $EC = AC$ and $CF = BC$. If $\angle D = 40^\circ$, then $\angle ACB = $?
In $\triangle DEF$ shown, points A, B, and C are taken on DE, DF, and EF respectively such that $EC = AC$ and $CF = BC$. If $\angle D = 40^\circ$, then $\angle ACB = $?
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Mark equal sides and use isosceles triangle properties to deduce equal angles for angle chasing.
Updated On: Aug 4, 2025
- 140
- 70
- 100
- None of these
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The Correct Option is B
Solution and Explanation
$EC = AC$ implies $\triangle AEC$ is isosceles with $\angle EAC = \angle ACE$. Similarly, $CF = BC$ implies $\triangle BCF$ is isosceles with $\angle FBC = \angle BCF$. Angle chasing in the geometry shows $\angle ACB = 70^\circ$.
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