| Directions: Each of the questions 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. [IDBI (SO) 2012] |
| 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 \[34{}^\circ \] more than the largest angle of the triangle. |
| II. Larger angle of the parallelogram is \[38{}^\circ \]more than its smaller angle. |
A) 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
B) 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
C) If the data in either statement I alone or in statement II alone are sufficient to answer the question
D) If the data in both the statements I and, II are not sufficient to answer the question
E) If the data in both the statements I and II together are necessary to answer the question
Correct Answer: C
Solution :
| From statement I |
| Larger angle of triangle \[=\frac{5}{3+5+4}\times 180{}^\circ =75{}^\circ \] |
| \[\therefore \]Larger angle of parallelogram \[=75{}^\circ +34{}^\circ =109{}^\circ \] |
| \[\therefore \]Smaller angle of parallelogram \[=180{}^\circ -109{}^\circ =71{}^\circ \] |
| From statement II, |
| Let the smaller angle of parallelogram \[=x\] |
| and the larger angle of parallelogram \[=x+38{}^\circ \] |
| Sum of two opposite angles of a parallelogram \[=180{}^\circ \] |
| \[x+x+38{}^\circ =180{}^\circ \] |
| \[\therefore \] \[x=\frac{180{}^\circ -38{}^\circ }{2}=\frac{142{}^\circ }{2}=71{}^\circ \] |
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