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B
2×180∘
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C
3×180∘
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D
4×180∘
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Solution
The correct option is C3×180∘
Step 1 : Select any vertex, in this case it is D.
Step 2 : Draw lines from the remaining vertices to D.
Step 3 : We can see that the pentagon is divided into 3 triangles, ΔDEA,ΔDAB,ΔDBC. Now to find ∠A+∠B+∠C+∠D+∠E, we need to find the sum of the interior angles of pentagon, which is nothing but the sum of the interiror angles of the 3 triangles.
Step 4 : Since we know that the sum of all angles in a triangle add up to 180∘. Thus, the sum of all interior angles of a pentagon is 3×180∘=540∘.