Question

# The angles of the quadrilateral are in the ratio 3 : 5 : 6 : 13. Find all the angles of the quadrilateral.

Hint: Here the ratios are let to the angles with variables and apply angle sum property of quadrilateral. Then find the answer of variables.

Let angles in the ratio 3 : 5 : 6 : 13 be a, b, c, d.
Let a = 3x, b = 5x, c = 9x, d = 13x
where x is any number
We know that
Sum of the angle of quadrilateral is ${360^ \circ }$
$\therefore a + b + c + d = {360^ \circ }$ (angle sum property of quadrilateral)
$\Rightarrow 3x + 5x + 9x + 13x = {360^ \circ }$
$\Rightarrow 30x = {360^ \circ }$
$\Rightarrow x = \dfrac{{360}}{{30}}$
$\therefore x = {12^ \circ }$
Hence the angles are
$a = 3x = 3 \times {12^ \circ } = {36^ \circ }$
$b = 5x = 5 \times {12^ \circ } = {60^ \circ }$
$c = 9x = 9 \times {12^ \circ } = {180^ \circ }$
$d = 13x = 13 \times {12^ \circ } = {156^ \circ }$

Note: In these types of questions in which the ratio is given for the angle we have to first let the angles with some variable and put in the condition of the question that is given in the question and find out the variable then put the variables and get the answer.