Year 8 Interactive Maths - Second Edition

Angle Sum of a Triangle

Activity 9.2

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°.

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

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.

Example 12

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

Example 13

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

Example 14

Find the value of each pronumeral in the following diagram.

Example 15

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

Exterior Angle of a Triangle

An exterior angle of a triangle is formed when any side is extended outwards.

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

Australian Business Number 53 056 217 611