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Question

Find the value A+B+C+D+E.

A
180
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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 C 3×180

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.

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