Two consecutive angles of a parallelogram are in the ratio 1: 3, then find the smaller angle.

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15 °

25 °

45 °

35 °

answer is C.

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Detailed Solution

Given, Ratio of two consecutive angles of a parallelogram=1: 3.
Let the angles be x, 3x where x is the common multiple.
Since the angles are consecutive angles of a parallelogram,

x + 3 x = 180 °

⇒ 4 x = 180 ° ⇒ x = 45 °

⇒ 3 x = 3 × 45 ° ⇒ 3 x = 135 °

Thus, the angles are

45 °, 135 °, 45 °, 135 °

.
The smaller angle is

45 °

.
Hence, the correct option is 3.

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