OGQR 2020: Question No. 222
The figure above shows a portion of a road map on which the measures of certain angles are indicated. If all lines shown are straight and intersect as shown, is road PQ parallel to road RS?
|Sub-Topic||Lines and Angles|
|Difficulty||Easy – Medium|
Steps 1 & 2: Understand Question and Draw Inferences
In this question, we are given:
- A portion of the roadmap
- Showing the measures of certain angles.
- All the lines shown in the figure are straight.
We need to find:
- Whether road PQ is parallel to road RS.
Per our conceptual understanding, when two parallel lines are cut by a transversal line then their corresponding angles are equal.
So, If PQ and RS are two parallel lines and line L1 as shown is the transversal line then the corresponding angles are equal.
- Hence, ∠1 = ∠2
- Or, c0 = 1800 – c0
- 2c = 180
- c = 90°
Therefore, if we get c = 90° then PQ and RS are parallel else PQ and RS are not parallel,
With this understanding, let us now analyse the individual statements.
Step 3: Analyse Statement 1
“b = 2a”
Per conceptual understanding, the sum of all the angles of a triangle is 180.
- Hence, a + b + c = 180
- a + 2a + c = 180
- 3a + c = 180
However, from the above equation, we can get many values of a and c.
Hence, statement 1 is not sufficient to answer the question.
Step 4: Analyse Statement 2
“c = 3a”
- a + b + c = 180
- a + b + 3a = 180
- b + 4a = 180
However, from the above equation, we can get many values of a and b.
- Hence, statement 2 is not sufficient to answer the question.
Step 5: Combine Both Statements Together (If Needed)
From statement 1:
- 3a + c = 180
From statement 2:
- c = 3a
Combining both the statements:
- 3a + 3a = 180.
From the above equation, we can find the value of a. Then we can find c.
Since we could find the answer by combining both the statements, option C is the correct answer.
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