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More Lessons for Grade 9
Math Worksheets
Examples, solutions, videos, worksheets, games, and activities to help Geometry students learn about the angle sum of a triangle.
What is the Triangle Sum Theorem?
The Triangle Sum Theorem states that the sum of the interior angles of a triangle equal 180°.
The following diagram shows an example of the Triangle Sum Theorem. Scroll down the page for examples and solutions.
Geometry Worksheets
Practice your skills with the following Geometry worksheets:
Printable & Online Geometry Worksheets
If we have a triangle with interior angles labeled as \(A\), \(B\), and \(C\), then the Triangle Sum Theorem can be expressed as the equation:
\(m\angle A+ m\angle B + m\angle C\) = 180°
Where \(m\angle\) denotes the measure of the angle in degrees.
Key Points about the Triangle Sum Theorem:
Triangle Angle Sum
The sum of the three angles in any triangle sum to 180 degrees. The importance of this fact in Geometry cannot be emphasized enough. The triangle angle sum theorem is used in almost every missing angle problem, in the exterior angle theorem, and in the polygon angle sum formula.
This video, discusses the sum of the interior angles of a triangle always equals 180 degrees. There are 4 example problems from easy, medium, medium-hard, and hard.
Angles of a Triangle - Triangle Sum Theorem with Algebra
Students learn the triangle sum theorem, which states that the sum of the measures of the angles of a triangle is 180 degrees. Students are then asked to solve problems related to the triangle sum theorem using Algebra.
Angle Sum of a Triangle
Geometry Word Problems - Angles of a Triangle
Example:
The measures of the angles of a triangle are in the ratio 2:5:8. Find the measure of each angle.
Examples of Using the Triangle Sum Theorem:
Example: Finding a Missing Angle
In a triangle, two angles measure 60° and 80°. Find the measure of the third angle.
Let the measures of the three angles be \(A = 60^\circ\), \(B = 80^\circ\), and \(C = x\).
Using the Triangle Sum Theorem:
60° + 80° + \(x\) = 180
140° + \(x\) = 180
\(x\) = 180° − 140°
\(x\) = 40°
So, the measure of the third angle is (40°).
Example: Using Algebra to Find Angles
The measures of the three angles of a triangle are y°, (y + 20)°, and (2y + 40)°. Find the value of y and the measure of each angle.
Using the Triangle Sum Theorem:
y + (y+20) + (2y+40) = 180
4y + 60 = 180
4y = 180 − 60
4y = 120
y = 120/4
y = 30
Now, substitute the value of y to find the measure of each angle:
First angle: y = 30°
Second angle: (30 + 20)° = 50°
Third angle: 2(30) + 40° = 100°
Check: 30° + 50° + 100° = 180°
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