Find the Missing Angle in an 80° Angle Problem

Linear Angle Pairs with Supplementary Properties

What is the size of the missing angle?

80

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 180∘180^\circ. Given that one angle is 80∘80^\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=180∘−80∘=100∘ \beta = 180^\circ - 80^\circ = 100^\circ

Therefore, the size of the missing angle is 100∘100^\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

Find the measure of the angle \( \alpha \)

949494AAABBBCCC92

FAQ

Everything you need to know about this question

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

+

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?

+

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?

+

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?

+

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?

+

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

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Angles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Angles in Parallel Lines

Find the Missing Angle in a 65° Circular Sector: Geometric Calculation
Click to solve
Solve for X: Finding Angle Measures with 20+100X in Parallel Lines
Click to solve

Sum and Difference of Angles

Triangle Angle Problem: Can 90, 115, and 35 Degrees Form a Triangle?
Click to solve
Triangle Classification: Analyzing Angles 53°, 117°, and 21°
Click to solve