Question

3) The ratio of the measures of angles of a quadrilateral in orders is
1:2:1:2. Find the measures of its angles & write the type of Quadrilateral​

Answer 1

Given:-

• The ratio of the measures of angles of a quadrilateral in orders is
• 1:2:1:2.

To Find:-

• Find the measures of its angles & write the type of Quadrilateral.

Concept used:-

• Sum of all angles of Quadrilateral is 360°

Now,

Let the ratio be "x"

So, The angles became x, 2x, x, 2x

Therefore,

→ x + 2x + x + 2x = 360°

→ 6x = 360

→ x = 360/6

→ x = 60

Hence, The Value of x is 60°

So, x = 60 and 2x = 120.

The value of angles of this Quadrilateral is 60, 120, 60 and 120.

→ It is a Parallelogram because opposite angles are equal.

Answer 2

Answer:

Let the angles be n , 2n , n and 2n of quadrilateral

• According to the Question :

⇒ Sum of all angles of Quadrilateral = 360

⇒ n + 2n + n + 2n = 360

⇒ 6n = 360°

⇒ n = 360° ÷ 6

⇒ n = 60°

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• Measures of the Angles :

◗ n = 60°

◗ 2n = 2(60°) = 120°

◗ n = 60°

◗ 2n = 2(60°) = 120°

If opposite angles are equal i.e. 60° = 60° and 120° = 120° , then the Quadrilateral is Parallelogram.