Question

the measures of the angles of a quadrilateral arein the ratio 3:2:5:8 find the measures of each of its triangle​

Answer 1

Appropriate Question :

The measures of the angles of a quadrilateral are in the ratio 3 : 2 : 5 : 8. Find the measures of each of its angle.

Given :

• Ratio of the angles of a quadrilateral = 3 : 2 : 5 : 8

To find :

• Measure of each of its angle

Solution :

Quadrilateral has 4 sides, 4 angles.

Let the four angles of the quadrilateral be 3x, 2x, 5x and 8x.

• First angle = 3x
• Second angle = 2x
• Third angle = 5x
• Fourth angle = 8x

Formula to be used,

★ Sum of interior angles of a polygon = (2n - 4) × 90°

where,

• n = number of sides of the polygon

Add all the angles which we have let and keep them equal to sum of interior angles of quadrilateral to find the value of x.

⇒ 3x + 2x + 5x + 8x = (2n - 4) × 90°

⇒ 18x = ((2 × 4) - 4) × 90°

⇒ 18x = (8 - 4) × 90°

⇒ 18x = 4 × 90°

⇒ 18x = 360°

⇒ x = 360°/18

⇒ x = 20°

The value of x = 20°

Substitute the value of x in all the angles which we have let.

• First angle = 3x = 3 × 20° = 60°
• Second angle = 2x = 2 × 20° = 40°
• Third angle = 5x = 5 × 20° = 100°
• Fourth angle = 8x = 8 × 20° = 160°

_________________________________

Let's verify :-

Add all the angles and if their sum is equal to 360° then the values are right.

⇒ 60° + 40° + 100° + 160°

⇒ 360°

Sum of angles of quadrilateral = 360°

Hence, verified.

Answer 2

Answer:

Answer is 40

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