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Lines and Angles - Drawing Angles

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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An angle is formed by two rays meeting at a common endpoint called the vertex. The standard unit of measurement is degrees (∘^\circ).

A basic angle diagram showing vertex and two rays.
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A protractor is used to measure and draw angles. It has two scales: the inner scale (0 to 180 CCW) and the outer scale (0 to 180 CW).

Diagram of a semi-circular protractor.
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To draw an angle like 60∘60^\circ, align the protractor's baseline with the ray and the center point with the vertex. Mark the point at 60∘60^\circ on the appropriate scale.

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Reflex angles (greater than 180∘180^\circ) can be drawn by subtracting the angle from 360∘360^\circ and drawing the remaining interior angle, then indicating the outer rotation.

📐Formulae

Acute Angle: 0∘<θ<90∘\text{Acute Angle: } 0^\circ < \theta < 90^\circ

Right Angle: θ=90∘\text{Right Angle: } \theta = 90^\circ

Obtuse Angle: 90∘<θ<180∘\text{Obtuse Angle: } 90^\circ < \theta < 180^\circ

Straight Angle: θ=180∘\text{Straight Angle: } \theta = 180^\circ

Reflex Angle: 180∘<θ<360∘\text{Reflex Angle: } 180^\circ < \theta < 360^\circ

Reflex Angle θ=360∘−Interior Angle\text{Reflex Angle } \theta = 360^\circ - \text{Interior Angle}

💡Examples

Problem 1:

Draw an angle of 120∘120^\circ and name its type.

Solution:

  1. Draw a ray BCBC. 2. Place the center of the protractor on BB and the baseline on BCBC. 3. Count from 0∘0^\circ on the scale that starts at CC and mark a point AA at 120∘120^\circ. 4. Join BABA. ∠ABC=120∘\angle ABC = 120^\circ.

Explanation:

Since 90∘<120∘<180∘90^\circ < 120^\circ < 180^\circ, the angle is an obtuse angle.

Problem 2:

How do you draw a reflex angle of 240∘240^\circ using a standard 180∘180^\circ protractor?

Solution:

360∘−240∘=120∘360^\circ - 240^\circ = 120^\circ 1. Draw a ray XYXY. 2. At point XX, draw an angle of 120∘120^\circ in the clockwise direction (below the ray). 3. The exterior/remaining part of the angle at the vertex XX represents 240∘240^\circ.

Explanation:

To draw a reflex angle, we calculate the difference between 360∘360^\circ and the reflex angle, then draw that remaining angle. The outer part is the required reflex angle.

Problem 3:

Identify the type of angle formed if the measure is 89.5∘89.5^\circ.

Solution:

It is an acute angle.

Explanation:

Any angle measuring less than 90∘90^\circ is classified as acute. Since 89.5∘<90∘89.5^\circ < 90^\circ, it fits this definition.

Problem 4:

Draw an obtuse angle PQR=135∘PQR = 135^\circ using a protractor.

An angle of 135 degrees labeled PQR.

Solution:

  1. Draw a ray QRQR.
  2. Place the center of the protractor on QQ and align the baseline with QRQR.
  3. Starting from 0∘0^\circ on the side of RR, find 135∘135^\circ on the scale and mark point PP.
  4. Join QPQP to form the angle.

Explanation:

Since 90∘<135∘<180∘90^\circ < 135^\circ < 180^\circ, this is an obtuse angle.

Problem 5:

Draw a right angle ABCABC and verify it using a protractor.

A 90 degree right angle labeled ABC.

Solution:

  1. Draw a horizontal ray BCBC.
  2. Use the protractor to mark a point AA at exactly 90∘90^\circ.
  3. Connect BB and AA. The angle ∠ABC\angle ABC will be 90∘90^\circ.

Explanation:

A right angle is exactly one-quarter of a full turn, represented by a square symbol at the vertex.