Question

find the measure of the four angles of a quadrilateeral if they are in the ration of 1:2:3:4
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Answer 1

⇒ Let the measure of angles be x,2x,3x and 4x.

We know that sum of measure of all four angles is 360°

∴ x+2x+3x+4x=360°

⇒ 10x=360°

⇒ x=36°

⇒ 2x=2×36°=72°

⇒ 3x=3×36°=108°

⇒ 4x=4×36°=144°

⇒ The measures of angles of quadrilateral are 36°,72°,108° and 144°

⇒ We can see measure of all 4 angles are different so, the given quadrilateral is trapezium.

Answer 2

Answer :-

36°, 72°, 108° and 144°

Explanation :-

Let the angles be x, 2x, 3x and 4x.

We know that,

Sum of all angles in Quad. = 360°

➞ x + 2x + 3x + 4x = 360°

➞ 10x = 360°

➞ x = 360 ÷ 10°

➞ x = 36°

So, The Angles are :-

• x = 36°
• 2x = 72°
• 3x = 108°
• 4x = 144°

Verification :-

Sum of all angles in Quad. = 360°

➞ 36 + 72 + 108 + 144 = 360°

➞ 108 + 108 + 144 = 360°

➞ 360° = 360°

LHS = RHS.

Hence, Verified.