Question

The angles of
quadrilateral are in the ratio
4:5:10:11. The angles are:​

Answer 1

Answer:

Let the angles be 4x, 5x, 10x and 11x

Sum of all the angles of a quadrilateral=360°

⇒4x+5x+10x+11x=360°

⇒9x+11x+10x=360°

⇒20x+10x=360°

⇒30x=360°

⇒x=360/30

⇒x=36/3

⇒x=12°

4x=4*12=48°

5x=5*12=60°

10x=10*12=120°

11x=11*12=132°

The angles are 48°, 60°, 120°, and 132°.

Answer 2

Given -

• Ratio of angles = 4 : 5 : 10 : 11

To find -

• Measure of each angles.

Formula used -

• Angle sum property of quadrilateral.

Solution -

In the question, we are provided with the ratio of angles of a quadrilateral, and we need to find the measure, of each angles. For that we will take a common ratio, then we will find the value of x, then we will find the measures, of each angles, by multiplying, the number with the value of x.

So -

Let the common ratio be termed as x

4 = 4x

5 = 5x

10 = 10x

11 = 11x

Now -

We will find the value, of x, by using, the angle sum property of a quadrilateral. For that first we will add a the rations, and will put it equal to 360°.

So -

Angle sum property = Sum of angle = 360°

On substituting the values -

Property = sum of angles = 360°

$\longrightarrow$4x + 5x + 10x + 11x = 360°

$\longrightarrow$ 30x = 360°

$\longrightarrow$ x = $\tt\dfrac{360}{30}$

$\longrightarrow$ x = 12

Now -

We will find the measures of all the angles, by multiplying 12, with every ratio.

4x = 4 × 12 = 48°

5x = 5 × 12 = 60°

10x = 10 × 12 = 120°

11x = 11 × 12 = 132°

Verification -

For verification, we will add up all the angles, and will put it equal to 360°.

48° + 60° + 120° + 132° = 360°

360° = 360°

$\therefore$ The measure of each angles is 48°, 60°, 120° and 132°

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