The angles of a quadrilateral are in the ratio 3: 4: 5: 6. The smallest of these angles is ____°.

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Detailed Solution

The angles of a quadrilateral are in the ratio 3: 4: 5: 6. The smallest of these angles is 60°.
Let the angles of the quadrilateral be 3x, 4x, 5x, 6x.
Now, as sum of interior angle of a quadrilateral is

360 °

3 x + 4 x + 5 x + 6 x = 360 °

18 x = 360 ° x = 360 ° 18 x = 20 °

Now, the angles of quadrilateral are,

3 x = 3 × 20 = 60 °

Second one,

4 x = 4 × 20 = 80 o

Third one,

5 x = 5 × 20 = 100 °

Fourth one,

6 x = 6 × 20 = 120 °

The smallest angle is

60 °

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