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Physics

Math Angles – Definition, Properties, Example,& Figures

Angles – Definition, Properties, Example,& Figures

Grade 4

Sep 20, 2022

Key Concepts

To understand angles and unit angles
To measure with unit angles
To measure and draw angles
To add and subtract angle measures

Understand Angles and Unit Angles

Angle:

An angle is the rotation of a ray from an initial point to a terminal point.

Types of Angles:

There are majorly six types of angles in geometry:

Acute angle: It lies between 0° to 90°.
Obtuse angle: It lies between 90° to 180°.
Right angle: The angle which is exactly equal to 90°.
Straight angle: The angle which is exactly equal to 180°.
Reflex angle: The angle which is greater than 180° and less than 360°.
Full rotation: The complete rotation of an angle equal to 360°.

Unit Angle:

An angle is measured with units called degrees (ᵒ).
An angle that turns through 1 / 360 of a circle is called a unit angle.

Examples of angles with their measurements:

Measure with Unit Angles

Unit angles are measured using a smaller angle to measure a larger angle by repeating the unit.

Unit angle

Example:

What is the measurement of the smaller angle formed by the clock hands when it is 5 o’clock?

Measure and Draw Angles

Measuring angles with a protractor

Angles are measured in degrees. The symbol for degrees is a small circle °.

Protractor

The full circle is 360° (360 degrees).
A half-circle or a straight angle is 180°.
A quarter-circle or a right angle is 90°.

How to measure an angle with a protractor?

A protractor is a tool that is used to measure and draw angles.

Protractor

Place the midpoint of the protractor on the vertex of the angle.
Line up one side of the angle with the line zero of the protractor
(Where you see the number 0).
Read the degrees where the other side crosses the number scale.

Example:

Draw ∠ABC=60° with a ruler and a protractor.

How to measure an angle with a protractor? 3

Draw a straight-line AB.
Place a dot at B.  This dot represents the vertex of the angle.
Place the center of the protractor at B and the baseline of the protractor along with the arm BA.
Find 60° on the scale and mark a small dot at the edge of the protractor.
Join the vertex B to the small dot with a ruler to form the second arm, BC, of the angle.
Mark the angle with a small arc as shown.

Add and Subtract Angle Measures

Finding the measure of an unknown angle by using the known measures.

If ∠ABD = 107°, what is the measure of ∠ABC?

We know that:

∠ABC + ∠CBD = ∠ABD

Plug in the known: n + 37° = 107°

Use the inverse operation to isolate the variable n = 107° – 37° = 70°

So, ∠ABC = 70°.

Exercise:

Use a protractor to draw an angle measure for 65⁰.
How many 60⁰ angles does it take to make a full turn?
How many degrees are in a twelfth of a full turn?
What fraction of the circle does a 120⁰ angle turn through?
What are the measures of an angle?
What are the 5 types of angles?
What is a zero angle?
Find the following missing angles.

Find the unknown angles from the figure below.

Find the unknown angles from the figure below.

What is the value of x?

What have we learnt:

To use and apply vocabulary associated with angles.
To identify examples of different types of angles.
To measure and draw angles with a protractor.
To understand angles and unit angles.
To add and subtract angle measures.

Concept Map:

Comments:

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