https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/proof-sum-of-measures-of-angles-in-a-triangle-are-180 2023-05-12T21:01:01.897246564Z Angles in a triangle sum to 180° proof The sum of the interior angle measures of a triangle always adds up to 180°. We can draw a line parallel to the base of any triangle through its third vertex. Then we use transversals, vertical angles, and corresponding angles to rearrange those angle measures into a straight line, proving that they must add up to 180°. Sal Khan video https://cdn.kastatic.org/googleusercontent/-_9m7sXFJ_DZGRlkqOTzZjy4vuXCY0hC1HrMevIJscQ5fyFoU8mekOV5C99_DXZ89kc-lHRN1rhn4WhPlCY4svU Angles in a triangle sum to 180° proof The sum of the interior angle measures of a triangle always adds up to 180°. We can draw a line parallel to the base of any triangle through its third vertex. Then we use transversals, vertical angles, and corresponding angles to rearrange those angle measures into a straight line, proving that they must add up to 180°. https://cdn.kastatic.org/ka-youtube-converted/6s1CI3uuhko.mp4/6s1CI3uuhko.mp4 268 Missing angles of triangles https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/e/triangle_angles_1 2026-03-31T08:44:48.259988263Z Find angles in triangles Find missing angle measures in triangles using the properties of general triangles, isosceles triangles, and equilateral triangles. Tomer Gal exercise https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/v/equilateral-and-isosceles-example-problems 2023-06-02T19:09:07.369858129Z Isosceles & equilateral triangles problems Isosceles triangles have two congruent sides and two congruent base angles. Equilateral triangles have all side lengths equal and all angle measures equal. We use these properties to find missing angles in composite figures. The problems are partly from Art of Problem Solving, by Richard Rusczyk. Sal Khan video https://cdn.kastatic.org/googleusercontent/9ixZ7rM7WmqajtAwRS3mCa1C3OYiLZrhx03UfUEQnQjc30b5gO_T-jECLSqXQYGBzsXjvVygQ_ea8Dxp8ySdVShc Isosceles & equilateral triangles problems Isosceles triangles have two congruent sides and two congruent base angles. Equilateral triangles have all side lengths equal and all angle measures equal. We use these properties to find missing angles in composite figures. The problems are partly from Art of Problem Solving, by Richard Rusczyk. https://cdn.kastatic.org/ka-youtube-converted/7FTNWE7RTfQ.mp4/7FTNWE7RTfQ.mp4 387 Missing angles of triangles https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-working-with-triangles/e/find-angles-in-isosceles-triangles 2026-04-01T18:54:25.495699557Z Find angles in isosceles triangles Find missing angles in isosceles triangles given just one angle. Ben Stenhaug exercise https://www.khanacademy.org/math/geometry/hs-geo-congruence/hs-geo-congruence-theorems/v/triangle-angle-example-1 2023-06-02T19:09:07.369858129Z Triangle exterior angle example An exterior angle is formed outside a triangle by extending a side. Its measure is equal to the sum of the two non-adjacent interior angle measures, thanks to the fact that all angle measures in a triangle add up to 180 degrees. Sal Khan video https://cdn.kastatic.org/googleusercontent/wLp2r0BNUUczDRaf0FEYElR-f16JqkKrGUXqmRV93k5fLjL3OY9okjdUz_do9oPMYQ6F7w7Q2DEqiHXfD9snNWDTPQ Triangle exterior angle example An exterior angle is formed outside a triangle by extending a side. Its measure is equal to the sum of the two non-adjacent interior angle measures, thanks to the fact that all angle measures in a triangle add up to 180 degrees. https://cdn.kastatic.org/ka-youtube-converted/hmj3_zbz2eg.mp4/hmj3_zbz2eg.mp4 363 Missing angles of triangles https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/v/triangle-angle-example-2 2023-06-02T19:09:07.369858129Z Worked example: Triangle angles (intersecting lines) Learn how to find unknown angles in triangles and intersecting lines. We use concepts like supplementary angles (angles that add up to 180°), vertical angles (opposite angles made by two crossing lines), and exterior angles (angles outside a triangle). There are lots of ways to think about this problem. Sal Khan video https://cdn.kastatic.org/googleusercontent/zGCHqinDWdb7VUFyJHlpvrcCfW_SjkBC1_ufAhF6ZiA9cRZUoXqIwEIpXHI_RdNUYD3l68G9LtVPPZuUkfjUcqA Worked example: Triangle angles (intersecting lines) Learn how to find unknown angles in triangles and intersecting lines. We use concepts like supplementary angles (angles that add up to 180°), vertical angles (opposite angles made by two crossing lines), and exterior angles (angles outside a triangle). There are lots of ways to think about this problem. https://cdn.kastatic.org/ka-youtube-converted/eTwnt4G5xE4.mp4/eTwnt4G5xE4.mp4 295 Missing angles of triangles https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/v/triangle-angle-example-3 2023-06-02T19:09:07.369858129Z Worked example: Triangle angles (diagram) We have a right triangle that's split into several smaller right triangles. The angle measures in any triangle always add up to 180 degrees. By using this fact and looking at complementary (adding up to 90 degrees) and supplementary (adding up to 180 degrees) angles, we can find the missing angle measures in the triangles. Sal Khan video https://cdn.kastatic.org/googleusercontent/o8ICTuKDwBsQ2PkEj-iWNEdxNrZgClsvpH1n894dLUVrbwhSxxAruyq7FeecsfnfL6j8l0CMmOtP0jkeiMbNvrs Worked example: Triangle angles (diagram) We have a right triangle that's split into several smaller right triangles. The angle measures in any triangle always add up to 180 degrees. By using this fact and looking at complementary (adding up to 90 degrees) and supplementary (adding up to 180 degrees) angles, we can find the missing angle measures in the triangles. https://cdn.kastatic.org/ka-youtube-converted/iqeGTtyzQ1I.mp4/iqeGTtyzQ1I.mp4 342 Missing angles of triangles https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/a/triangle-angles-review 2024-06-17T03:51:36.667583972Z Triangle angles review Review the basics of triangle angles, and then try some practice problems. article https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-triangle-angles/e/angles_2 2026-03-31T08:44:48.259988263Z Finding angle measures using triangles Use your knowledge about angles to find missing angle measures in various complex situations. David Lai exercise