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Year 7 Interactive Maths - Second Edition


Angle Sum of a Triangle

Activity 2

Task 1

Step 1:

Draw a triangle ABC and cut out the three angles.

triangle ABC


Step 2:

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

A straight angle is 180.

Angle A + Angle B + Angle C = 180
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 3

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

triangle ABC

Solution:

Let the missing angle be x.
Since the angle sum of a triangle = 180, x = 80

So, the missing angle is 80.


Example 4

Find the values of the pronumerals x and y in the following diagram:

triangle ABC

Solution:

Use the fact that the base angles of an isosceles triangle are equal and the angle sum of a triangle is 180 to find x = 40 and y = 100.


Example 5

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

Find x in triangle ABC.

Solution:

Using the fact that the base angles of an isosceles triangle are equal, we find that x = 6


Example 6

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

triangle ABC

Solution:

After determining ABC is an equilateral triangle, we find x = 12


Example 7

Find the values of the pronumerals x and y in the following diagram:

triangle ABC

Solution:

After determining ABC is an equilateral triangle, we find x = 18

After determining ABC is an equilateral triangle, we find y = 9


Example 8

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

triangle ABC

Solution:

Using the angle sum of a triangle = 180, we find x = 6


Key Term

angle sum of a triangle


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