krit.club logo

Shapes and Angles - Angle Tester

Grade 5CBSE

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

🔑Concepts

•

An Angle Tester is a simple tool made of two strips (like cardboard or metal) joined at one end with a pivot (like a split pin). It can be opened to different widths to check if an angle is a right angle, less than a right angle, or more than a right angle.

An angle tester opened to a perfect L-shape representing a right angle.
•

When the angle tester opens like the letter 'L', it is called a Right Angle. Its measure is exactly 90∘90^{\circ}.

•

If the angle tester opens less than the 'L' shape, it is an Acute Angle, which is less than 90∘90^{\circ}.

An angle tester opened narrowly, showing an acute angle.
•

If the angle tester opens wider than the 'L' shape, it is an Obtuse Angle, which is more than 90∘90^{\circ} but less than 180∘180^{\circ}.

•

You can use the corner of your notebook or a square paper as a 'readymade' angle tester to check corners of objects around you.

📐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}.

Problem 3:

Meena uses her angle tester on a pair of scissors. The blades are opened such that the tester shows an angle wider than an 'L' shape. If the angle is 35∘35^{\circ} more than a right angle, what is its measure?

An obtuse angle of 125 degrees.

Solution:

90∘+35∘=125∘90^{\circ} + 35^{\circ} = 125^{\circ}

Explanation:

A right angle is 90∘90^{\circ}. Since the angle is 'more than a right angle' by 35∘35^{\circ}, we add 35∘35^{\circ} to 90∘90^{\circ} to get 125∘125^{\circ}. This is an obtuse angle.

Problem 4:

Look at the hands of a clock showing 2:00. Use your understanding of an angle tester to determine if the angle between the hands is a right angle, more than a right angle, or less than a right angle. Also, calculate the angle if each hour mark represents 30∘30^{\circ}.

A clock face showing 2:00, forming an acute angle.

Solution:

2×30∘=60∘2 \times 30^{\circ} = 60^{\circ} It is less than a right angle.

Explanation:

At 2:00, the minute hand is at 12 and the hour hand is at 2. The gap covers 2 hour divisions. Since each hour is 30∘30^{\circ}, the total angle is 2×30∘=60∘2 \times 30^{\circ} = 60^{\circ}. Since 60∘<90∘60^{\circ} < 90^{\circ}, the angle tester would show it is less than an 'L' shape (acute).