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Shapes and Angles - Angle Tester

Grade 5CBSE

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

🔑Concepts

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An angle is formed when two lines or rays meet at a common point called a vertex. Visually, this looks like the corner of a room, the tip of a pencil, or the point where two hands of a clock meet.

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A Right Angle is an angle that measures exactly 90∘90^{\circ}. It looks like the perfect corner of the letter 'L' or the edge of a textbook. When using an angle tester, the two arms will align perfectly with the horizontal and vertical lines of the corner.

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An Angle Tester (also known as a divider) is a simple tool made of two strips of cardboard or plastic fixed at one end with a drawing pin. It can be opened or closed to match any angle. If the tester opens to form a shape like the letter 'L', the angle being measured is a right angle.

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Acute Angles are those that are smaller than a right angle, measuring less than 90∘90^{\circ}. Visually, the gap between the arms of the angle tester will be narrower than an 'L' shape, similar to a partially opened pair of scissors or a slice of pizza.

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Obtuse Angles are larger than a right angle but smaller than a straight line. They measure more than 90∘90^{\circ} and less than 180∘180^{\circ}. In an angle tester, the arms will be spread wider than the 'L' shape, looking like a hand fan spread open or a reclining chair.

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A Straight Angle is formed when the two rays of the angle point in exactly opposite directions, creating a flat line. It measures exactly 180∘180^{\circ}. Visually, it looks like two right angles joined together, making the angle tester arms form a single straight horizontal or vertical line.

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In geometric shapes, the 'Angle Tester' helps identify properties. For example, a square and a rectangle have four right angles (90∘90^{\circ} each) at their corners. In a triangle, although the angles can vary (acute, right, or obtuse), the sum of all three internal angles will always be 180∘180^{\circ}.

📐Formulae

Right Angle = 90∘90^{\circ}

Acute Angle < 90∘90^{\circ}

Obtuse Angle > 90∘90^{\circ} and < 180∘180^{\circ}

Straight Angle = 180∘=2×90∘180^{\circ} = 2 \times 90^{\circ}

Sum of angles in a triangle = 180∘180^{\circ}

Sum of angles in a quadrilateral = 360∘360^{\circ}

💡Examples

Problem 1:

A student uses an angle tester on the corner of a square window. The tester opens to form a perfect 'L' shape. What is the measurement and name of this angle?

Solution:

  1. The problem states the tester forms a perfect 'L' shape.
  2. By definition, an 'L' shape represents a Right Angle.
  3. A right angle always measures exactly 90∘90^{\circ}.

Explanation:

We identify the angle by comparing the physical shape of the opening to the standard 'L' shape used in angle testers.

Problem 2:

If an angle is found to be 30∘30^{\circ} smaller than a right angle, calculate its value and classify it.

Solution:

Step 1: Identify the value of a right angle: 90∘90^{\circ}. Step 2: Subtract 30∘30^{\circ} from the right angle: 90∘−30∘=60∘90^{\circ} - 30^{\circ} = 60^{\circ} Step 3: Compare 60∘60^{\circ} to 90∘90^{\circ}. Since 60∘<90∘60^{\circ} < 90^{\circ}, the angle is an Acute Angle.

Explanation:

We use the fixed value of a right angle as a reference to find the unknown angle and then classify it based on whether it is smaller or larger than 90∘90^{\circ}.