Why Triangle Angles Sum to 180 Degrees
Written by Adi Ackerman, Head Teacher
"Why Triangle Angles Sum to 180 Degrees" is written for 8th Grade (Ages 13-14), and it covers Common Core 8.G.A.5. A 7th grader who is already steady on geometry can use it too, and an older student can use it as a short review.
8th grade math worksheet: use a line through B parallel to AC to see why triangle angles add up to 180°, then find x. Answer key included. Part of our angles in triangles geometry collection. Aligned to Common Core standards.
How do I use this worksheet?
Use Why Triangle Angles Sum to 180 Degrees to introduce the fact, then the missing angle and exterior angle sheets for practice. Save the algebra sheets and Angle Chains With Triangles and Straight Lines for multi step work.
What students will practice
- Students will use alternate interior angles to match angles at B with angles A and C.
- Students will complete sentences that show the three angles form a straight angle.
- Students will apply the 180° fact to find x in triangles.
Name Angle Pairs Formed by a Transversal
Find Angles on Parallel Lines Cut by a Transversal
Solve for x With Transversal Angle Pairs
Triangle Angle Sum, Find the Missing Angle
Quadrilateral Angle Sums From Two Triangles
Triangle Interior Angles, Solve for the Variable
Exterior Angle of a Triangle, Find the Measure
Exterior Angles, Solve for the Variable
Curriculum Links
Common Core State Standards
Geometry · 8th Grade
Standard: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
View all 8.G.A.5 worksheets →Find this in the curriculum
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FAQ
How do I use this angles in triangles worksheet?
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Use Why Triangle Angles Sum to 180 Degrees to introduce the fact, then the missing angle and exterior angle sheets for practice. Save the algebra sheets and Angle Chains With Triangles and Straight Lines for multi step work.
What does this worksheet teach?
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Use a line through B parallel to AC to see why triangle angles add up to 180°, then find x. The directions on the page read: Line DE passes through B and is parallel to AC. Write the measures of angles 1, 2 and 3. Then complete each sentence and find x in each triangle. An answer key is included.
Can I use this angles in triangles worksheet for homeschool or classroom?
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Yes, both. We made it for 8th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.
How do you find the missing angle of a triangle?
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Add the two known angles and subtract the sum from 180°. In a triangle with angles of 58° and 72°, the missing angle is 50°.
What is an exterior angle of a triangle?
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It is the angle formed outside a triangle when one side is extended. It equals the sum of the two interior angles that are not next to it, and it forms a straight angle with the interior angle beside it.
How do you find the angle sum of a quadrilateral?
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Draw a diagonal to split it into two triangles. Each triangle has 180°, so the quadrilateral's angles add up to 360°. Quadrilateral Angle Sums From Two Triangles builds this step by step.
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Name Angle Pairs Formed by a Transversal
Find Angles on Parallel Lines Cut by a Transversal
Solve for x With Transversal Angle Pairs
Triangle Angle Sum, Find the Missing Angle
Quadrilateral Angle Sums From Two Triangles
Triangle Interior Angles, Solve for the Variable
Exterior Angle of a Triangle, Find the Measure
Exterior Angles, Solve for the Variable