Vertical Angles: Identifying Alpha (α) at Line Intersections

Right Angles with Perpendicular Line Intersections

What type of angle is α \alpha ?

αα

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What type of angle is α \alpha ?

αα

2

Step-by-step solution

Remember that an acute angle is smaller than 90 degrees, an obtuse angle is larger than 90 degrees, and a straight angle equals 180 degrees.

Since the lines are perpendicular to each other, the marked angles are right angles each equal to 90 degrees.

3

Final Answer

Straight

Key Points to Remember

Essential concepts to master this topic
  • Rule: Perpendicular lines always form four 90-degree right angles
  • Technique: Look for the small square symbol marking α = 90°
  • Check: All four angles at intersection add to 360°: 90° × 4 = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing right angles with straight angles
    Don't assume α is 180° just because lines cross = wrong angle type! A straight angle forms a straight line, but right angles form perpendicular intersections with square corners. Always look for the square symbol indicating 90°.

Practice Quiz

Test your knowledge with interactive questions

Identify the angle shown in the figure below?

FAQ

Everything you need to know about this question

How can I tell if an angle is really 90 degrees?

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Look for the small square symbol in the corner of the angle! This symbol always marks a right angle. Also, perpendicular lines create four identical right angles at their intersection.

What's the difference between right and straight angles?

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A right angle measures exactly 90° and looks like a square corner. A straight angle measures 180° and forms a straight line. Think: right = corner, straight = line!

Are all angles at perpendicular intersections the same?

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Yes! When two lines are perpendicular, all four angles formed are right angles measuring exactly 90°. This is always true for perpendicular lines.

Why isn't α an acute or obtuse angle?

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Acute angles are less than 90°, and obtuse angles are greater than 90°. Since the diagram shows perpendicular lines with square symbols, α measures exactly 90°, making it a right angle.

How do I remember the different angle types?

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  • Acute: Less than 90° (sharp and small)
  • Right: Exactly 90° (square corner)
  • Obtuse: Greater than 90° but less than 180° (wide and blunt)
  • Straight: Exactly 180° (forms a line)

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