The angles of the quadrilateral are in the ratio 3 : 5 : 6 : 13. Find all the angles of the quadrilateral.
Answer
380.7k+ views
Hint: Here the ratios are let to the angles with variables and apply angle sum property of quadrilateral. Then find the answer of variables.
Complete step-by-step answer:
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.
Complete step-by-step answer:
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.
Recently Updated Pages
Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

Which planet is known as the red planet aMercury bMars class 6 social science CBSE

Which state has the longest coastline in India A Tamil class 10 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE
