When you see multiple angles arranged along a straight line in a diagram, your first thought should be that their sum is 180°. This is a very common geometric principle tested in exams.
The relationship cannot be determined from the information given.
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The Correct Option isB
Solution and Explanation
Step 1: Understanding the Concept:
The question involves finding the value of an unknown angle, x, from a geometric diagram. The diagram shows three adjacent angles, \(2x^\circ\), \(120^\circ\), and \(x^\circ\), whose outer rays form a straight line. Angles on a straight line sum to 180 degrees. Step 2: Key Formula or Approach:
The sum of angles that form a straight line is 180°. We can set up an equation using the given angles.
\[ 2x + 120 + x = 180 \] Step 3: Detailed Explanation:
The three angles lie along a straight line, so their sum must be 180°.
\[ 2x^\circ + 120^\circ + x^\circ = 180^\circ \]
Combine the terms with x:
\[ 3x + 120 = 180 \]
Subtract 120 from both sides:
\[ 3x = 180 - 120 \]
\[ 3x = 60 \]
Divide by 3:
\[ x = 20 \]
The value of x is 20. Comparison:
Column A: \(x = 20\)
Column B: 80
Since \(20<80\), the quantity in Column B is greater. Step 4: Final Answer:
The quantity in Column B is greater.
