Adjacent Angles Problem: Finding Pairs That Sum to 180 Degrees

Linear Pair Angles with Complementary Recognition

The sum of adjacent angles is 180 degrees.

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Step-by-step video solution

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00:00 Is the sum of adjacent angles equal to 180?
00:03 Let's draw adjacent angles
00:09 Adjacent angles complete a straight angle (180)
00:15 Therefore, the sum of adjacent angles equals 180
00:19 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

The sum of adjacent angles is 180 degrees.

2

Step-by-step solution

To solve this problem, let's first understand the concept of adjacent angles. Adjacent angles share a common vertex and a common side. When two adjacent angles are formed by two intersecting lines, they often form what is known as a linear pair.

According to the Linear Pair Postulate, if two angles form a linear pair, then the sum of these adjacent angles is 180180 degrees. This is because these angles lie on a straight line, effectively forming a straight angle, which measures 180180 degrees.

Let's apply this knowledge to the statement in the problem:
The statement says, "The sum of adjacent angles is 180 degrees." In the context of the Linear Pair Postulate, this is indeed correct as adjacent angles that create a linear pair sum to 180180 degrees.

Therefore, when the statement refers specifically to linear pairs, it is true.

Thus, the solution to the problem is True.

3

Final Answer

True

Key Points to Remember

Essential concepts to master this topic
  • Linear Pair Rule: Adjacent angles on straight line sum to 180180 degrees
  • Recognition: Look for shared vertex and side forming straight line
  • Check: Measure both angles: 120°+60°=180°120° + 60° = 180° confirms linear pair ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all adjacent angles sum to 180 degrees
    Don't assume every pair of adjacent angles adds to 180°180° = wrong conclusions about angle relationships! Only adjacent angles forming a linear pair (on a straight line) sum to 180°180°. Always check if the angles form a straight line before applying this rule.

Practice Quiz

Test your knowledge with interactive questions

If one of two corresponding angles is a right angle, then the other angle will also be a right angle.

FAQ

Everything you need to know about this question

What makes two angles adjacent?

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Adjacent angles must share a common vertex and a common side, but their interiors cannot overlap. Think of them as angles that are 'next to' each other.

Do all adjacent angles add up to 180 degrees?

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No! Only adjacent angles that form a linear pair sum to 180°180°. This happens when the angles lie on a straight line together.

How can I tell if adjacent angles form a linear pair?

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Look for these clues:

  • The angles share a vertex and side
  • Their non-common sides form a straight line
  • Together they make a straight angle

What if I see adjacent angles that don't add to 180°?

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That's completely normal! Adjacent angles around a point can add to 360°360°, or they might be part of a triangle where they add to less than 180°180°.

Can adjacent angles be equal to each other?

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Yes! If two adjacent angles form a linear pair and are equal, each angle measures 90°90°. These are called right angles.

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