Year 8 Interactive Maths - Second Edition

Angle Sum of a Triangle

Activity 9.2

Task 1

Step 1:

Draw a triangle ABC and cut out the three angles.

Step 2:

Rearrange the three angles to form a straight angle on a straight line.

So, the angle sum of a triangle is 180°.

Task 2

To investigate if this works for all triangles, repeat the above process for four different triangles.

Task 3

Copy and complete the following statements:
a.  The three angles of a triangle can be arranged to form a ……….. angle.
b.  The sum of three angles in a triangle is ………..

Finding the Third Angle of a Triangle

If the measurements of two angles of a triangle are known, then the third angle can be calculated.

Example 10

Calculate the size of the missing angle in the following triangle.

Solution:

Let the missing angle be x.

So, the missing angle is 84º.

Example 11

Find the value of each pronumeral in the following diagram.

Solution:

Example 12

Find the value of the pronumeral x in the following diagram.

Solution:

Example 13

Find the value of the pronumeral x in the following diagram.

Solution:

Example 14

Find the value of each pronumeral in the following diagram.

Solution:

Example 15

Find the value of the pronumeral x in the following diagram.

Solution:

Exterior Angle of a Triangle

Clearly, the exterior angle ACD and the adjacent interior angle ACB are supplementary.  That is:

Example 16

Find the value of each pronumeral in the following diagram.

Solution:

Key Terms

angle sum of a triangle, exterior angle of a triangle