Question

The angle which makes a linear pair with an angle of \(61^{\circ}\) is :

• A. \(29^{\circ}\)
• B. \(61^{\circ}\)
• C. \(119^{\circ}\)
• D. \(122^{\circ}\)

Hint:

Linear pair angles always sum to \(180^{\circ}\).
To subtract \(61\) from \(180\) quickly in your head, subtract \(60\) first to get \(120\), then subtract \(1\) to get \(119^{\circ}\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question is from Geometry, specifically concerning lines, angles, and their relations.
We need to find the angle that forms a linear pair with a given angle of \(61^{\circ}\).

Step 2: Key Formula or Approach:
Two angles form a linear pair if they are adjacent angles formed by two intersecting lines.
By the Linear Pair Postulate, the sum of the angles in a linear pair is always equal to \(180^{\circ}\) (they are supplementary).
If the two angles are \(\alpha\) and \(\beta\):
\[ \alpha + \beta = 180^{\circ} \]

Step 3: Detailed Explanation:
Let the given angle be \(\alpha = 61^{\circ}\).
Let the unknown angle that forms a linear pair with it be \(\beta\).
Using the linear pair property:
\[ \alpha + \beta = 180^{\circ} \]
Substitute the value of \(\alpha\):
\[ 61^{\circ} + \beta = 180^{\circ} \]
Subtract \(61^{\circ}\) from both sides to find \(\beta\):
\[ \beta = 180^{\circ} - 61^{\circ} \]
\[ \beta = 119^{\circ} \]

Step 4: Final Answer:
The angle that makes a linear pair with \(61^{\circ}\) is \(119^{\circ}\).