Question

The angles of quadrilateral ABCD are in the ratio 2:3:5:8. Find all anglrs of quadrilateral​

Answer 1

Answer:

• Measures of angles are 40° , 60° , 100° & 160° respectively .

Step-by-step explanation:

According to the Question

It is given that,

• Ratio of angles of Quadrilateral 2:3:5:8

Let the ratio of angles be 2x : 3x : 5x : 8x respectively .

As we know that Sum of all angles in a quadrilateral is 360° .

• Sum of all angles = 360°

On substituting the value we get

↠ 2x + 3x + 5x + 8x = 360°

↠ 18x = 360°

↠ x = 360°/18

↠ x = 20°

So, the measures of angles

→ 2x = 2×20° = 40°

→ 3x = 3×20° = 60°

→ 5x = 5×20° = 100°

→ 8x = 8×20° = 160°

• Hence, the measures of angles are 40° , 60° , 100° & 160° respectively .

Answer 2

Answer:-

• 40°, 60°, 100° and 180° are the different measures of angles.

Given:-

• Ratio of angles of a quadrilateral.

To find:-

• Measure of those angles.

Solution:-

We know that the Sum of interior angles of a quadrilateral is equal to 360°.

So, we get that the ratio of the angles sum up to 360°.

Therefore,

$\bf{ \implies\angle1 + \angle2 + \angle3 + \angle4 = 360 \degree}$

Let the angles be "x"

Henceforth on putting the values we get:-

$\large\underline{\bf{ \longmapsto2x + 3x + 5x + 8x = 360 \degree}}$

$\large\underline{\bf{ \longmapsto18x = 360 \degree}}$

$\large\underline{\bf{ \longmapsto x = \frac{360 \degree}{18} }}$

$\large\underline{\bf{ \longmapsto x = 20 \degree}}$

Now on calculating the measures of angles we get:-

First angle:-

$\large\underline{\bf{ \implies2x = 2 \times 20 \degree}}$

$\large\underline{ \boxed{\bf{ \maltese \: \: \: \: 2x = 40 \degree}}}$

Second angle:-

$\large\underline{\bf{ \implies3x = 3 \times 20 \degree}}$

$\large\underline{ \boxed{\bf{ \maltese \: \: \: \: \: \:3x = \: 60 \degree}}}$

Third angle:-

$\large\underline{\bf{ \implies5x = 5 \times 20 \degree}}$

$\large\underline{ \boxed{\bf{ \maltese \: \: \: \: \: \: \: \: 5x = 100 \degree}}}$

Fourth angle:-

$\large\underline{\bf{ \implies8x = 8 \times 20 \degree}}$

$\large\underline{\boxed{ \bf{ \maltese \: \: \: \: \: \: \: \: 8x = 160 \degree}}}$

______________________________________