Topics
12. Geometry
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Stage 3

12.11 Angles on a straight line

Lesson
Practice
Lesson

Are you ready?

Being able to  identify an angle  can help us in this lesson. Let's try this problem to review.

Examples

Example 1

Select the obtuse angle:

A
A straight angle
B
A right angle
C
An obtuse angle
D
An acute angle
Worked Solution
Create a strategy

Use this image to help you:

A circle with markings at 0, 90 degrees, and 180 degrees. Ask your teacher for more information.

Rotate each angle so that one arm lies over the start.

Apply the idea

The answer is Option C.

An obtuse angle
Idea summary

A full revolution is made up of 360 degrees, a single degree is written 1\degree.

Angle typeAngle size
\text{Acute angle}\text{Larger than } 0 \degree, \text{smaller than } 90\degree.
\text{Right angle}90\degree
\text{Obtuse angle}\text{Larger than } 90\degree, \text{smaller than } 180\degree.
\text{Straight angle}180\degree
\text{Reflex angle}\text{Larger than } 180\degree, \text{smaller than } 360\degree.
\text{Full revolution}360\degree

Angles on straight lines

Let's learn more about angles on a straight line.

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Examples

Example 2

Find the size of the missing angle.

The image shows two angles that make up a straight angle. Ask your teacher for more information.
Worked Solution
Create a strategy

Subtract the given angle from 180\degree.

Apply the idea

The two angles should add up to 180\degree since they lie on a straight line. So to find the missing angle we can subtract 129\degree from 180\degree .

\displaystyle \text{Missing angle}\displaystyle =\displaystyle 180-126Subtract 126 from 180
\displaystyle =\displaystyle 54\degree
The image shows two angles that make up a straight angle. Ask your teacher for more information.
Idea summary

Angles on a straight line always add up to 180 degrees.

Outcomes

MA3-16MG

measures and constructs angles, and applies angle relationships to find unknown angles

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