Question

1.
The angles of quadrilateral are in the ratio 3:5:9:13. Find all the angles of the
quadrilateral​

Answer 1

SOLUTION

Given,

The angles of quadrilateral are in the ratio = 3:5:9:13

Let the ratio be x

We know that sum of Quadrilateral= 360°

=) 3x+ 5x+ 9x+13x= 360°

=) 30x= 360°

=) x= 360/30

=) x= 12°

Now,

1st angle= 3x= 3×12° = 36°

2nd angle= 5x= 5× 12°= 60°

3rd angle= 9x= 9× 12°= 108°

4th angle= 13x= 13× 12°= 156°

hope it helps ☺️⬆️

Answer 2

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Let the common ratio be x

Then angles will be= 3x, 5x, 9x, 13x

As, we know that the sum of the angles of a quadrilateral is 360°

Now, according to the question

3x+5x+9x+13x= 360°

⟹30x= 360°

$\bold{\implies \: x = \frac{360}{30} }$

⟹x= 12°

Now,

3x= 3×12= 36°

5x= 5×12= 60°

9x= 9×12= 108°

13x= 13× 12= 156°

Verification:-

Sum of angles = 360°

36°+60°+108°+156°= 360

⟹96°+264°= 360°

⟹360°= 360°

L.H.S=R.H.S