Question

if four angles of quadrilateral are in ratio 2:19::2:37. find all four angles of quadrilateral.​

Answer 1

Given:

Ratio of angles of quadrilateral

• 2 : 19 : 2 : 37

What To Find:

We have to find the angles of the quadrilateral.

Property:

Sum of interior angle of quadrilateral = 360°

Solution:

Let's take x as the common multiple.

Using the property,

⇒ Sum of interior angle of quadrilateral = 360°

Substitute the values,

⇒ 2x + 19x + 2x + 37x = 360°

Add the terms,

⇒ 60x = 360°

Take 60 to RHS,

⇒ $\sf{x = \dfrac{360}{60}}$

Cancel the zeros,

⇒ $\sf{x = \dfrac{36}{6}}$

Divide 36 by 6,

⇒ x = 6

Now, substitute the value,

1. First angle = 2x = 2 × 6 = 12°
2. Second angle = 19x = 19 × 6 = 114°
3. Third angle = 2x = 2 × 6 = 12°
4. Fourth angle = 37x = 37 × 6 = 222°