Find the Missing Angle in an 80° Angle Problem

Linear Angle Pairs with Supplementary Properties

What is the size of the missing angle?

80

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the value of the empty angle
00:03 The angles are adjacent, forming a straight angle (sum to 180)
00:06 Subtract the known angle from 180 to find the empty angle
00:08 And that's the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the size of the missing angle?

80

2

Step-by-step solution

To find the size of the missing angle, we will use the property that the sum of angles on a straight line is 180180^\circ. Given that one angle is 8080^\circ, we can calculate the missing angle using the following steps:

  • Step 1: Recognize that the given angle α=80\alpha = 80^\circ and the missing angle β\beta form a straight line.
  • Step 2: Use the angle sum property for a straight line: α+β=180 \alpha + \beta = 180^\circ
  • Step 3: Substitute the known value: 80+β=180 80^\circ + \beta = 180^\circ
  • Step 4: Solve for the missing angle β\beta: β=18080=100 \beta = 180^\circ - 80^\circ = 100^\circ

Therefore, the size of the missing angle is 100100^\circ.

3

Final Answer

100°

Key Points to Remember

Essential concepts to master this topic
  • Rule: Angles on a straight line always sum to 180°
  • Technique: Subtract given angle from 180°: 180° - 80° = 100°
  • Check: Add both angles together: 80° + 100° = 180° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing supplementary with complementary angles
    Don't think angles on a line add to 90° = wrong answer of 10°! Complementary angles (90°) are for right angles, not straight lines. Always remember straight lines total 180°.

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

Why do angles on a straight line add to 180°?

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A straight line forms a straight angle, which by definition measures exactly 180°. When you split this into two or more angles, they must add up to the original 180°.

What's the difference between supplementary and complementary angles?

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Supplementary angles add to 180° (straight line), while complementary angles add to 90° (right angle). Remember: Supplementary = Straight = 180°!

Can I have more than two angles on a straight line?

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Yes! You can have 3, 4, or more angles on a straight line. The key rule remains the same: all angles must add up to 180° total.

How do I identify if angles form a straight line?

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Look for angles that share a common vertex and whose sides form a straight line. In diagrams, this appears as angles sitting next to each other on a line.

What if I get a negative answer?

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Check your work! Angles are always positive. If you get negative, you likely subtracted in the wrong direction or misread the given angle measure.

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