If two angles form a linear pair, then the measures of the angles add up to 180∘

General
1

if two angles form a linear pair, then the measures of the angles add up to 180∘ .

2

If two angles form a linear pair, then the measures of the angles add up to 180° .

Answer: Yes, that statement is correct. Let’s delve into what it means for two angles to form a linear pair and why their measures add up to 180°.

Understanding Linear Pairs

Definition: A linear pair of angles is a pair of adjacent angles formed when two lines intersect. The two angles are adjacent, meaning they share a common side and a common vertex, and their non-common sides form a straight line (or are collinear).

Why Do the Measures Add Up to 180°?

When two angles form a linear pair, they are supplementary by definition. Here’s a step-by-step explanation:

  1. Straight Line Property: The non-common sides of the two angles form a straight line. A straight line measures 180°.

  2. Angle Addition Postulate: The Angle Addition Postulate states that if a point lies on the interior of an angle, the sum of the measures of the two adjacent angles formed is equal to the measure of the original angle.

  3. Application to Linear Pairs: In the case of a linear pair, the original “angle” is the straight line, which measures 180°. Therefore, the sum of the measures of the two adjacent angles (which form the linear pair) must be 180°.

Mathematical Representation

Let’s denote the two angles in the linear pair as ∠A and ∠B.

Since they form a linear pair:

\text{m}∠A + \text{m}∠B = 180°

Where:

  • ( \text{m}∠A ) is the measure of angle A.
  • ( \text{m}∠B ) is the measure of angle B.

Example

Suppose angle ∠A measures 120°. To find the measure of angle ∠B in the linear pair:

\text{m}∠A + \text{m}∠B = 180°

Substituting the known value:

120° + \text{m}∠B = 180°

Solving for ( \text{m}∠B ):

\text{m}∠B = 180° - 120°
\text{m}∠B = 60°

Therefore, ∠A and ∠B, which form a linear pair, have measures that add up to 180°, confirming the statement.

Conclusion

In conclusion, the statement by Questionmatic is accurate. When two angles form a linear pair, their measures indeed add up to 180°. This property is a fundamental concept in geometry, reflecting the supplementary nature of linear pairs.