Question

(i) What do you mean by convex and concave Quadrilaterals?

(ii) The angles of a Quadrilateral ABCD are in the ratio of $3:4:5:6$. Find the largest angle.

Answer 1

(i) A convex quadrilateral is a quadrilateral whose diagonals lie in the interior of the Quadrilateral.

If any of the diagonals is not in the interior of the Quadrilateral, it is called a Concave Quadrilateral.

(ii) The sum of all the angles of a Quadrilateral $={360}^{\circ }$

The ratio of the angles is $3:4:5:6$

Let the angles be $3x,4x,5x$ and $6x$

$3x+4x+5x+6x={360}^{\circ }$

$\Rightarrow 18x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{18}={20}^{\circ }$

Thus, the angles are $3\times {20}^{\circ },4\times {20}^{\circ },5\times {20}^{\circ }\text{and}6\times {20}^{\circ }$

$\Rightarrow {60}^{\circ },{80}^{\circ },{100}^{\circ }\text{and}{120}^{\circ }$

So, the largest angle is ${120}^{\circ }$