Two angles in a triangle are 45° and 65°. Find the third.
- The known angles total 110°.
- Subtract from 180°.
Answer: 70°
Triangle Sum Theorem Worksheets for 10th Grade
Apply the triangle angle sum theorem to find missing angle measures.
Learn the skill
Finding missing angles in triangles
The interior angles of a triangle in Euclidean geometry sum to 180°. An exterior angle formed by extending a side equals the sum of the two nonadjacent interior angles.
A method you can use
- Identify the three interior angles; distinguish exterior labels from interior ones.
- Write a sum of 180° or an equivalent exterior-angle equation.
- Solve for the unknown and check all angle measures are positive.
Worked examples
A triangle has angles x°, 2x°, and 3x°. Find all three.
- x + 2x + 3x = 180, so 6x = 180.
- x = 30; substitute into each expression.
Answer: 30°, 60°, 90°
An exterior angle is 120° and one remote interior angle is 50°. Find the other remote interior angle.
- The two remote interior angles sum to 120°.
- Subtract 50 from 120.
Answer: 70°
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. A triangle has angles 35° and 75°. Find the third.
Show answer and explanation
70°
180 − 35 − 75 = 70.
2. An isosceles triangle has vertex angle 40°. Find each base angle.
Show answer and explanation
70°
The equal base angles share 180 − 40 = 140 degrees.
About Triangle Sum Theorem
Triangles are the most fundamental polygon and the workhorse of geometric reasoning. In this unit, students master the Triangle Angle Sum Theorem, prove triangle congruence and similarity using multiple criteria, explore the rich properties of triangle segments and centers, and investigate inequalities governing triangle side lengths and angles. Mastery of triangles is prerequisite knowledge for virtually every subsequent topic in geometry and trigonometry.
The Triangle Angle Sum Theorem is one of the most frequently used facts in all of geometry. It connects directly to parallel line theory and is prerequisite knowledge for congruence proofs, trigonometry, and polygon angle calculations.
What Your Child Will Learn
- State and apply the Triangle Angle Sum Theorem (angles sum to 180 degrees)
- Find missing angle measures in triangles using the theorem
- Apply the Exterior Angle Theorem to solve for unknown angles
- Classify triangles as acute, right, or obtuse using their angle measures
- Write algebraic equations from angle sum conditions and solve for unknown variables
Worksheets by Difficulty
Start with Easy worksheets to build confidence, then progress to Medium and Hard as your student masters each level.
Understanding the Difficulty Levels
Worksheets 1-3 are Easy level — designed to build confidence with simpler numbers and straightforward problem types. Great for introducing the concept or reviewing basics.
Worksheets 4-7 are Medium level — offering a moderate challenge with larger numbers, varied question types, and more problems per worksheet.
Worksheets 8-10 are Hard level — featuring the most challenging problems including multi-step questions, missing values, and real-world applications.
Tips for Parents & Teachers
1
Encourage your student to write proof outlines in everyday language first, then translate to formal two-column notation.
2
CPCTC (Corresponding Parts of Congruent Triangles are Congruent) is used constantly — make sure your student can explain it in their own words.
3
Similarity is the key to trigonometry. Ask: "Why does the sine ratio give the same answer for a 30-degree angle regardless of triangle size?" The answer is similarity.
4
Triangle inequality can be checked at home: can you make a triangle with three straws of lengths 3, 5, and 9 inches? Try it!
Frequently Asked Questions
What will my child learn from triangle sum theorem worksheets?
These 10th Grade triangle sum theorem worksheets help students practice triangles, angles, geometry. Each worksheet provides structured practice with clear instructions and varied problem types.
How often should my 10th Grade student practice triangle sum theorem?
Consistent practice works best. We recommend 10-15 minutes of focused practice 3-4 times per week. Start with Easy worksheets and progress to Medium and Hard as your student builds confidence.
Are these triangle sum theorem worksheets free to print?
Yes, all 10th Grade triangle sum theorem worksheets on K12Worksheets are completely free. You can download and print as many as you need for home or classroom use — no signup required. Each worksheet includes a printable answer key on a separate page.
How do I know which triangle sum theorem worksheet to start with?
Begin with the Easy worksheets (Worksheets 1–3) to assess your student's current skill level. If they complete these confidently, move to Medium (Worksheets 4–7). Reserve Hard worksheets (Worksheets 8–10) for students who have mastered the basics. If your student struggles with Easy worksheets, revisit prerequisite topics first.