Direction: Each of the question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement are sufficient to answer the question.
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What is the smaller angle of a parallelogram ?
I. Ratio between the angles of a triangle is 3 : 5 : 4 and the larger angle, of the parallelogram is 34 ° more than the largest angle of the triangle.
II. Larger angle of the parallelogram is 38° more than its smaller angle.
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- If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
- If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
- If the data in either Statement I alone or in Statement II alone are sufficient to answer the question
- If the data in both the Statements I and II are not sufficient to answer the question
- If the data in both the Statements I and II together are necessary to answer the question
Correct Option: C
From Statement I.
Let the ratio proportion is x.
some of angle of triangle = 180 °
3x + 5x + 4x = 180 °
12x = 180 °
x = 180 ° /12
x = 15 °
Largest angle of triangle
= 5x = 5 x 15
= 75 °
∴ Larger angle of parallelogram
= 75 ° + 34 °
= 109 °
∴ Smaller angle of parallelogram
= 180 ° - 109 °
= 71 °
From Statement II,
Let the smaller angle of parallelogram be = x
and the larger angle of parallelogram = x + 38 °
Sum of two opposite angles of a parallelogram = 180 °
x + x + 38 ° = 180 °
∴ 2x = 180 ° - 38°
∴ 2x = 142°
∴ x = 142° / 2
∴ x = 71 °
