Question

The angle of a quadrilateral is in the ratio \[3:5:9:13\] . Find all the angles of the quadrilateral in degrees.
A. \[36,60,108,156\]
B. \[36,70,108,156\]
C. \[36,60,118,156\]
D.None of these

Answer 1

Hint: In order to solve this question first, we have to assume one factor from which the ratio comes out. So multiplying all the ratios with the factor and then all of them are added together and equated to the sum of all the angles of a quadrilateral. The Sum of all angles of a quadrilateral is \[360\] degree.

Complete step-by-step answer:
Given,
The ratio of all the angles of the quadrilateral is \[3:5:9:13\] .
To find,
All the values of the angle of quadrilateral.
Let the fraction that is canceled is \[x\]
On multiplying this factor we get the original value of the angles.
The angles of the quadrilateral are \[3x,5x,9x,13x\]
Sum of all the values of the quadrilateral is \[360\] .
From here we get the equation:
 \[3x + 5x + 9x + 13x = 360\]
On further solving
 \[30x = 360\]
On dividing by \[30\] both sides.
 \[\dfrac{{30x}}{{30}} = \dfrac{{360}}{{30}}\]
On further calculations
 \[x = 12\]
This is the factor that is multiplied by the ratio in order to get the angles.
The angles of the quadrilateral are.
 \[3x,5x,9x,13x\]
Now on multiplying by the value of \[x\] we get.
 \[3 \times 12,5 \times 12,9 \times 12,13 \times 12\]
On further calculations
 \[36,60,108,156\]
So, the correct answer is “ \[36,60,108,156\] ”.

Note: To solve these types of questions you must know the sum of all the angles of different-different polynomials and assume a factor that is canceled while using finding the ratio. Then multiply that factor with the ratio and add all of them and equate it to the sum of all the angles of that polynomial and try to find the value of that factor. Multiply by the ratio in order to get the final answer of the angles of the polynomial. A regular polygon has all its interior angles equal to each other