Question

20. The angles of a quadrilateral are
in the ratio 2: 3: 4: 6. The angles are
respectively.​

Answer 1

Answer :-

Angles are 48°, 72°, 96° and 144°

Explanation :-

Given : The angles of a quadrilateral are

in the ratio 2: 3: 4: 6.

To Find : All the angles.

Solution :

Let the angles be 2x, 3x, 4x and 6x.

And, We know that,

Angle Sum Property of Quad. = 360°

So, Put the Values.

⇒ 2x + 3x + 4x + 6x = 360°

⇒ 5x + 10x = 360°

⇒ 15x = 360°

⇒ x = 360 ÷ 15.

⇒ x = 24.

Therefore,

• 1st Angle = 2x = 48°
• 2nd Angle = 3x = 72°
• 3rd Angle = 4x = 96°
• 4th Angle = 6x = 144°

Verification :-

Angle Sum Property of Quad. = 360°

⇒ 2x + 3x + 4x + 6x = 360°

⇒ 48° + 72° + 96° + 144° = 360°

⇒ 120° + 240° = 360°

⇒ 360° = 360°

LHS = RHS.

Hence, Verified.

Answer 2

Answer:

The angles are 48°, 72°,96°and 144° respectively...

Step-by-step explanation:

Question:

The angles of a quadrilateral are in the ratio 2: 3: 4: 6. The angles are respectively......

Given:

• ✍️ Angles of quadrilateral are in the Ratios= 2:3:4:6

Assume:

• ✍️ Let the ratios be 2x, 3x, 4x and 6x respectively

Theorem:

Before moving on to the solution, you need to remember the theorem......

The sum of all the angles of the quadrilateral is 360°

Solution:

✍️ According to the theorem,

• ✍️ 2x+3x+4x+6x=360°
• ✍️ 15x=360°

$\implies\boxed{\frak{\purple{x = 24}}}$

Now, To find all the four angles, we need to substitute the value of x=24 in the following ratios.

Substitution:

• ✍️2x= 2(24)= 48°
• ✍️ 3x= 3(24)= 72°
• ✍️ 4x= 4(24)= 96°
• ✍️ 6x= 6(24)= 144°

Final answer:

The angles are 48°, 72°,96°and 144° respectively...

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