Question

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

Answer 1

Answer:

156°,108°,60°and36°

Step-by-step explanation:

Let angles be 3x ,5x,9xand 13x

By angle sum property of a quadrilateral

3x+5x+9x+13x=360°

30x=360°

x=360÷30

=12°

Therefore angles afre 13x=156°

3x=36°

5x=60°

9x=108°

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Answer 2

Answer :-

The angles of quadrilateral is

Step-by-step explanation

To Find :-

• The angles of quadrilateral.

★ Solution

Given that,

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

Assumption

Let us assume the angles of quadrilateral as 3x, 5x, 9x and 13x.

As we know that,

Sum of all interior angles of quadrilateral measures 360°

Therefore,

• 3x + 5x + 9x + 13x = 360°

→ 3x + 5x + 9x + 13x = 360

→ 8x + 9x + 13x = 360

→ 17x + 13x = 360

→ 30x = 360

→ x = 360/30

→ x = 36/3

→ x = 12

After evaluating, we got the value of x as 12.

The angles of quadrilateral are :-

• 3x = 3*12 = 36°
• 5x = 5*12 = 60°
• 9x = 9*12 = 108°
• 13x = 13*12 = 156°

Hence, The angles of quadrilateral is 36°, 60°, 108° and 156°.

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V E R I F I C A T I O N :-

• 3x + 5x + 9x + 13x = 360

L.H.S = 3x + 5x + 9x + 13x

R.H.S = 360

By simplifying, The L.H.S :-

→ 3x + 5x + 9x + 13x

→ 36 + 60 + 108 + 156

→ 36 + 60 + 264

→ 36 + 324

→ 36

Now, L.H.S = R.H.S

Hence, Verified!