Problem Set 24 – Naming Angles, Vertex and ArmsClass 5 Maths · Chapter 6 Angles · Problem Set 24 – Maharashtra Board

Summary: Problem Set 24 – Naming Angles, Vertex and Arms

An angle is made when two lines start from the same point. A right angle is like the corner of a book, an acute angle is smaller than it and an obtuse angle is bigger.

The common point where the two lines meet is the vertex. The two lines are the arms of the angle.

We name an angle with three letters. The vertex letter always goes in the middle: ∠XYZ has vertex Y and arms YX and YZ.

The same angle can be read from either end: ∠XYZ and ∠ZYX are the same angle. The sign ∠ means 'angle'.

A protractor is a half-circle tool for measuring and drawing angles. Its curved edge has 180 equal parts; each part is 1 degree (1°).

Key points to remember

• Vertex = the point where the two arms meet
• Arms = the two lines that make the angle
• Angle names use 3 letters; the middle letter is the vertex
• ∠PQR and ∠RQP name the same angle
• The sign ∠ is read as 'angle'
• A protractor is shaped like a half circle
• Its curved edge has 180 equal parts, each 1°
• A protractor has two scales: 0 to 180 from the right and 0 to 180 from the left

Problem Set 24 – Naming Angles, Vertex and Arms – Notes

1. Right, acute and obtuse — a quick look back

• A right angle looks like the corner of a page or a square tile.
• An acute angle is narrower than a right angle — like the two hands of a clock at 1 o'clock.
• An obtuse angle is wider than a right angle but not a straight line — like the clock hands at 5 o'clock.
• At 3 o'clock and at 9 o'clock, the clock hands make a right angle.

2. Vertex and arms

• Think of a pair of scissors that is open. The screw where the blades meet is like the vertex.
• The two blades are like the arms of the angle.
• In a drawing, the arms are lines that both start at the vertex. Their ends are marked with capital letters.

3. Naming an angle

• Take one letter from the end of the first arm, then the vertex letter, then a letter from the end of the second arm.
• The vertex letter must sit in the middle. ∠XYZ means the vertex is Y.
• You may start from either arm: ∠XYZ and ∠ZYX are two names for one angle.
• Instead of writing the word 'angle', we write the sign ∠.

4. Meet the protractor

• A protractor is a half circle made of plastic or metal. We use it to measure angles and to draw angles of a given size.
• Its curved edge is split into 180 equal small parts. Each small part is one degree, written 1°.
• The middle point of its straight edge is called the centre of the protractor.
• The straight line on the protractor through the centre is the baseline (line of reference).

5. Two scales on one protractor

• The outer and inner rows of numbers both go from 0 to 180.
• One row starts with 0 on the right side and counts up towards the left (anticlockwise).
• The other row starts with 0 on the left side and counts up towards the right (clockwise).
• When you measure, always start counting from the 0 that lies on the same side as the arm of the angle.

Formulas at a glance

Key terms

Problem Set 24 – Naming Angles, Vertex and Arms – Flashcards

Read the question, answer it in your head, then tap the card to check. 10 cards.

Problem Set 24 – Naming Angles, Vertex and Arms – MCQ Quiz

10 questions. Tap an option — you will see at once if it is right and why.

How to study Problem Set 24 – Naming Angles, Vertex and Arms

⏱ About 20 minutes

1. Learn (5 min)
   Learn the words vertex and arms, and the three-letter rule for naming.
2. Name (10 min)
   Draw 3 angles, put letters on them and name each one in two ways. Look closely at a protractor.
3. Practise (5 min)
   Do the 4 'Try it yourself' sums, take the quiz and play 🎮 Play.