Worksheet Triangle Sum and Exterior Angle Theorem Answer Key: Understanding the Triangle Sum and Exterior Angle Theorem in Geometry

The Triangle Sum Theorem states that the sum of the interior angles of any triangle is always 180 degrees. The Exterior Angle Theorem says that an exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. These foundational theorems are essential in solving many geometry problems. Below is a typical answer key for a worksheet focused on both the Triangle Sum and Exterior Angle Theorems:

Tips 1:

As a designer, I find that visualizing triangle problems—by drawing precise sketches or using digital tools—crucially aids understanding. Digital design platforms can help you experiment with geometric layouts, making abstract math more concrete. Using a room planner or design tool, geometry can be easily represented for practical, real-world applications, whether you're arranging furniture or designing spaces with specific angles in mind.

Typical Answer Key Example:

1. Find the missing angle:

If one triangle has angles 65°, 75°, and x, then:

65° + 75° + x = 180°

x = 180° - (65° + 75°) = 40°

2. Exterior Angle Theorem:

Given triangle with interior angles of 60°, 50°, and x; and the exterior angle adjacent to 50° is y.

Then y = 60° + x.

If x = 70°, then y = 60° + 70° = 130°

3. Find the value of the marked exterior angle if the two non-adjacent interior angles are 45° and 85°:

Exterior angle = 45° + 85° = 130°

4. A triangle has angles (2x)°, (3x)°, and (x+10)°. Find x:

2x + 3x + (x+10) = 180°

6x + 10 = 180

6x = 170

x = 28.33°

5. Find the missing angle in a triangle if two angles are 90° and 45°:

90° + 45° + x = 180°

x = 45°

FAQ

Q: What is the Triangle Sum Theorem?

A: The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Q: How does the Exterior Angle Theorem work?

A: The Exterior Angle Theorem says that an exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles.

Q: Can I use these theorems for all types of triangles?

A: Yes, both the Triangle Sum Theorem and the Exterior Angle Theorem apply to all triangles: scalene, isosceles, and equilateral.

Q: Why are these theorems important in real life?

A: They’re essential for fields like architecture, engineering, and design because they help in constructing accurate angles and layouts.

Q: How can I visually check my angle calculations?

A: Drawing a triangle to scale, or using a digital design solution, can help confirm your angles sum properly and exterior angles match the calculated values.