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Properties of 2D shapesEstimation
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Here we will learn about the different types of angles including how to identify angle types and estimate them.
There are also types of angles worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
An angle is formed between two lines (rays) meeting around a common point (vertex).
They are measured in degrees and have the degree sign °.
An angle is indicated by the symbol (∠) followed by three capital letter with the middle letter as the vertex of the angle.
The name of the angle on the left is ∠ABC or ∠CBA.
There are generally
Acute Angles – An acute angle is an angle that is less than 90°:
Obtuse Angles – An obtuse angle is an angle greater than 90° but less than 180°:
Reflex Angles – A reflex angle is greater than 180° but less than 360°:
Right Angles – A right angle is 90° and has a small square inside the angle to indicate it is a right angle. The two rays in a right angle are perpendicular:
It is also important to note:
Straight Angle – A straight angle is one-half a whole turn and is
Complete turn – A full rotation is
Did you know the word angle comes from the Latin word angulus, which means a corner?
In order to find the angle type:
What type of angle is seen below?
On examination the above angle is closest to
2Determine if it is less or greater than the angle in step
3Use the definitions of the different angles to determine the angle type.
Since the angle is less than
An angle is
Determine whether the angle is closer to 90°, 180°, or 360°.
The angle is closest to
Determine if it is less or greater than the angle in step 1.
Use the definitions of the different angles to determine the angle type.
Since the angle is less than
Estimate the size of the missing angle.
On observation, the angle is an obtuse angle as it is greater than 90° but less than 180°. Your estimate must fall within this range.
In the above example, the given angle is closer to the
Particularly when it comes to reflex angles make sure to look at the angle indicated by the arc and not the acute angle.
When measuring or estimating angles your answer must always be given in degrees.
1. State the name of the angle in the diagram below:
The mark in the corner tells us that this is 90 degrees, so it is a right angle.
2. State the the name of the angle in the diagram below:
This angle is greater than 90 degrees, and less than 180 degrees, so it is an obtuse angle.
3. An angle is 87.8° . What type of angle is it?
This angle is less than 90 degrees, so it is an acute angle.
4) An angle is 298° . What type of angle is it?
This angle is greater than 180 degrees and less than 360 degrees, so it is a reflex angle.
5. Which estimate best describes the size of the angle below:
The angle is between 270° and 360° , so 290° is a reasonable estimate.
6. Which estimate best describes the size of the angle below:
The angle is between 180° and 270° , so 240° is a reasonable estimate.
1. (a) What is the special name for the angle below:
(b) Estimate the size of the angle above.
Accept any answer between 0° and 90°
2. Below is a trapezium.
(a) Mark the acute angle with an X.
(b) Mark the obtuse angle with an O.
(c) Mark the right angle with an R.
Marks ∠ABC with an X.
Marks ∠DCB with an O.
Marks either ∠BAD or ∠CDA with an R.
a) What is the mathematical name of the shape below?
b) Estimate the size of the obtuse angles in the shape above.
Accept any answer between 90° and 180°.
You have now learned how to:
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