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The angles of a quadrilateral are within the ratio 3: 4: 5: 6. Which angle from these angles is the largest?

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90 °

120 °

150 °

102 °

answer is B.

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Detailed Solution

Given the ratio of the angles of the quadrilateral is 3: 4: 5: 6.
Let the angles of the quadrilateral are

3 x, 4 x, 5 x, and 6 x .

By using the angle sum property of a quadrilateral, we get,

3 x + 4 x + 5 x + 6 x = 360 ° ⇒ 18 x = 360 ° ⇒ x = 360 ° 18 ° ⇒ x = 20 °

Therefore we have got,

3 x = 3 × 20 = 60 ° 4 x = 4 × 20 = 80 ° 5 x = 5 × 20 = 100 ° 6 x = 6 × 20 = 120 °

All the angles of the quadrilateral are

60 °, 80 °, 100 °, and 120 ° .

Hence the largest of these angles is

120 °,

and so option (2) is the correct option.

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