Question

four angles of a quadrilateral are in the ratio 1:2:3:4 difference between the greatest and the smallest angle is.
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Answer 1

Answer:

Given the four angles of a quadrilateral are in the ratio 1:2:3:4

Then Let the angles are x,2x,3x and 4x

We know that total of four angles of a quadrilateral =360⁰

∴x+2x+3x+4x=360

⇒10x=360

⇒x=36⁰

hence the measures of angles are 36⁰

,72⁰ ,108⁰ ,144⁰

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Answer 2

Since angles are in ratio 1:2:3:4

So,

Let angles be,

A = 1x = x

B = 2x

C = 3x

D = 4x

Since sum of angles of quadrilateral is 360°

So,

A+B+C+D = 360

x + 2x + 3x + 4x = 360

10x = 360

x = 360/10

x = 36

Therefore angles are,

A = x = 36°

B = 2x = 2×36 = 72°

C = 3x = 3×36 = 108°

D = 4x = 4×36 = 144°

Here greatest angle is D and smallest angle is A.

So, difference between them = D - A

= 144 - 36

= 108°