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Question

Statement 1:  Sum of the interior angles of a quadrilateral is 360

Statement 2:  A diagonal divides the quadrilateral into two triangles. The sum of angles of a triangle is 180


  1. Both statements are wrong.

  2. Both statements are correct and statement 2 has sufficient information to prove statement 1

  3. Statement 1 is correct and statement 2 wrong

  4. Both statements are correct but statement 2 doesn’t have sufficient information to prove statement 1


Solution

The correct option is B

Both statements are correct and statement 2 has sufficient information to prove statement 1


Let ABCD be a quadrilateral and AC be a diagonal.

We know that,

DAC+ACD+D = 180  (1)

Similarly, in ABC,

CAB+ACB+B = 180 (2)

Adding (1) and (2), we get,

DAC+ACD+D+CAB+ACB+B = 180+180 = 360

But, DAC+CAB=A
and, ACD+ACB=C

So, A+D+B+C = 360

i.e., the sum of the angles of a quadrilateral is 360.

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