The angles of a quadrilateral are in the ratio 1:2 :3:4. Determine the measure of the smallest angle and choose the option which represents the same.

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72°

144°

36°

18°

answer is C.

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Detailed Solution

Given, the angles of a quadrilateral are in the ratio 1:2 :3:4.
The angle sum property of a quadrilateral states that the sum of all interior angle measures of a quadrilateral is always

360 °

.
Now, based on the given ratio of the interior angles, let us assume that the interior angle measures of the given quadrilateral are

x ∘, 2 x ∘, 3 x ∘

and

4 x ∘

.
So, by the angle sum property of a quadrilateral, we have,

x ° + 2 x ° + 3 x ° + 4 x ° = 360 ° 10 x ° = 360 ° x = 36010 x = 36 °

Now, as the smallest angle in terms of ratio is

x ∘

, so the smallest angle measure of the quadrilateral is

36 ∘

.
Hence, the correct option is (3).

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