Question

The angles of a quadrilateral are in the ratio 2:3:5:8. Find the smallest and greatest angle.

Answer 1

Hello, Buddy!!

||Required Solution||

Given,

Ratio of Angles of a Quadrilateral = 2:3:5:8

→ 2x+3x+5x+8x = 360°

• Sum of Interior Angles of a Quadrilateral is 360°

→ 18x = 360°

→ x = 360°/18

→ x = 20°

Smallest Angle is 2x

→ 2(20°)

→ 40°

Greatest Angle is 8x

→ 8(20°)

→ 160°

• Smallest Angle ☞ 40°
• Greatest Angle ☞ 160°

@MrMonarque♡

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Answer 2

Answer:

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

A.T.Q

2x+3x+5x+8x=360° (Sum of all angles of quadrilateral is 360°)

=> 18x =360°

=> x = 360°÷18

=> x = 20°

Then,

2x = 2×20°=40°

3x = 3×20° =60°

5x = 5×20°=100°

8x = 8×20°=160°

Therefore, The smallest angle is 40° and greatest angle is 160°.