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More Lessons for Grade 6

Math Worksheets

Examples, solutions, videos, worksheets, stories and songs to help Grade 6 students learn that the angles of a triangle always add up to 180 degrees and to use that concept to find missing angle in a triangle.

### Sum of Angles in a Triangle

To illustrate that the sum of the interior angles of a triangle is the same
for all triangles in a visual manner, we can create several large triangles
of varying shapes and sizes on construction paper. Use a
protractor to trace an arc between the arms of all three angles of each
triangle. Cut the corners off each triangle along the
curved arc. Arrange the
three corners so that
they are all joined at
the vertex forming
a straight angle.

We will see that when the three corners are arranged at a common vertex the three angles form a half circle (180°). By using triangles of various sizes and shapes we can see that the sum of the three interior angles will always be 180° for all triangles.

Cutting the corners of the triangles in an arc and labelling the vertices with letters or symbols will avoid confusion as to which vertices need to be adjacent when aligning the angles. The curved edges also provide a clearer visual that the three interior angles of any given triangle form a half circle.

We can also measure the interior angles of the triangles we used in the above activity using a protractor and then find the sum. We may notice that in some cases their sum does not

equal 180° exactly but is very close. This could be due to error in measurement.

We observe that no matter how we change the shape and size of the triangle, the sum of the interior angles will always be 180°.

**Triangle Angle Sum**

Visual illustrations of the sum of triangle angles.

### Missing Angle in a Triangle

We can extend this concept of triangle sum to find a missing angle in a given triangle when
two other angle measures are known. The unknown angle measure can be
determined by subtracting the sum of the
two known angles from 180°.

Worksheets to find the missing angle in a triangle:

Missing Angles in a Triangle 1

Missing Angles in a Triangle 2

**Missing Angles in Triangles**

How to find missing angles in scalene triangles, isosceles triangles and equilateral triangles?**Angles of Triangles Add Up To 180 Degrees**

Ex: Could a triangle have the given angle measures?

a) 115, 35, 30

b) 45, 45, 60**Angles of Triangles Add Up To 180 Degrees**

Since all three angles add up to 180 degrees, you can find the missing angle by subtraction.

**Angles of Triangles Add Up To 180 Degrees**

Find two missing angles that are equal.**How to Find the Missing Angle in a Triangle?**
**How to find a missing angle in a triangle?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Grade 6

Math Worksheets

Examples, solutions, videos, worksheets, stories and songs to help Grade 6 students learn that the angles of a triangle always add up to 180 degrees and to use that concept to find missing angle in a triangle.

We will see that when the three corners are arranged at a common vertex the three angles form a half circle (180°). By using triangles of various sizes and shapes we can see that the sum of the three interior angles will always be 180° for all triangles.

Cutting the corners of the triangles in an arc and labelling the vertices with letters or symbols will avoid confusion as to which vertices need to be adjacent when aligning the angles. The curved edges also provide a clearer visual that the three interior angles of any given triangle form a half circle.

We can also measure the interior angles of the triangles we used in the above activity using a protractor and then find the sum. We may notice that in some cases their sum does not

equal 180° exactly but is very close. This could be due to error in measurement.

We observe that no matter how we change the shape and size of the triangle, the sum of the interior angles will always be 180°.

Visual illustrations of the sum of triangle angles.

Worksheets to find the missing angle in a triangle:

Missing Angles in a Triangle 1

Missing Angles in a Triangle 2

How to find missing angles in scalene triangles, isosceles triangles and equilateral triangles?

Ex: Could a triangle have the given angle measures?

a) 115, 35, 30

b) 45, 45, 60

Since all three angles add up to 180 degrees, you can find the missing angle by subtraction.

Find two missing angles that are equal.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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