Question

3)The angles of Quadrilateral are in
the ratio of 1:4:5:8. Find the angles
.Also identify the Quadrilateral.

Answer 1

Given :–

• The angles of Quadrilateral are in ratio of 1:4:5:8.

To Find :–

1. Angles of the quadrilateral.
2. Identify the quadrilateral.

Solution :–

1} Let, the angles of quadrilateral be 1x, 4x, 5x, and 8x.

We know that,

Sum of the angles of the quadrilateral is 360°.

So,

→ 1x + 4x + 5x + 8x = 360°

→ 18x = 360°

→ x = $\frac{\cancel{360}}{\cancel{18}}$

→ x = 20°

Hence,

The angles are :–

1. 1x = 1 × 20° = 20°
2. 4x = 4 × 20° = 80°
3. 5x = 5 × 20° = 100°
4. 8x = 8 × 20° = 160°

2} We know that,

✏️ Quadrilateral is a polygon.

✏️ It has four sides.

✏️ It has four angles.

✏️ It has only one pair of parallel side.

✏️ We already find the four angles of the quadrilateral.

So,

→ 1x + 4x + 5x + 8x = 360°

→ 20° + 80° + 100° + 160°

→ 100° + 260°

→ 360°

Yes, this is a Quadrilateral.

Answer 2

Answer:

20°, 4×20°=80°, 5×20°=100° and 8×20°=160°

Step-by-step explanation:

Let the angles of the quadrilateral be x,4x,5x and 8x .

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

Therefore , x + 4x + 5x + 8x = 360°

or 18x = 360°.

Therefore , 360°/18 = 20°

So, the four angles of th quadrilateral are

20° , 4×20°=80° , 5×20°=100° and 8×20°=160°.