Question

Statement 1: Sum of the interior angles of a quadrilateral is ${360}^{\circ }$.

Statement 2: A diagonal divides the quadrilateral into two triangles. The sum of angles of a triangle is ${180}^{\circ }$.

• A. Both statements are correct and statement 2 has sufficient information to prove statement 1.
• B. Both statements are correct but statement 2 doesn’t have sufficient information to prove statement 1.
• C. Statement 1 is correct and statement 2 wrong.
• D. Both statements are wrong.

Answer 1

The correct option is A

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

Let ABCD be a quadrilateral with AC as its diagonal.

$\angle DAC+\angle ACD+\angle D$ = ${180}^{\circ }$ (1) ($\because$ sum of angles in triangle)

Similarly, in $△ABC$,

$\angle CAB+\angle ACB+\angle B$ = ${180}^{\circ }$ (2)($\because$ sum of angles in triangle)

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

$\angle DAC+\angle ACD+\angle D+\angle CAB+\angle ACB+\angle B$ = ${180}^{\circ }+{180}^{\circ }$ = ${360}^{\circ }$

But, $\angle DAC+\angle CAB=\angle A$
and, $\angle ACD+\angle ACB=\angle C$

So, $\angle A+\angle D+\angle B+\angle C$ = ${360}^{\circ }$

i.e., the sum of the angles of a quadrilateral is ${360}^{\circ }$.

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