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

Look at the angles shown in the figure below.

What is their relationship?

\( \)αβ

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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