Angles on Lines and Triangles and Area by Cutting | Six Minutes: Math Kangaroo, Part 16

Six Minutes: Math Kangaroo, Part 16: Angles on Lines and Triangles and Area by Cutting: Three rules that crack every angle puzzle; then Area by Cutting Straight-line angles, triangle angle sums, and the outside-angle shortcut turn one given angle into all the others. Includes a worked example checked two ways and the classic outside-angle trap. Then: Any strange shape becomes easy when you cut it into rectangles and triangles. Learn the two area formulas, the perpendicular-height rule, and a box-and-subtract check. Chapters 0:00 Introduction 0:23 Straight lines 0:43 Triangles 1:01 Isosceles shortcut 1:19 Worked example 1:56 Trap 2:16 Recap 2:30 Area by Cutting 2:40 Cut it up 3:09 See the cut 3:37 Worked example 4:18 Trap 4:34 Recap 4:50 Thanks for watching Practice problems 1. In triangle LMN, angle L is 55 degrees and side MN is stretched to point P, making outside angle MNP equal to 130 degrees. Find angle M. (Answer: 75 degrees, since angle LNM = 180 − 130 = 50, and angle M = 180 − 55 − 50 = 75.) 2. Triangle XYZ is isosceles with XY = YZ. The outside angle at Y along a straight line is 140 degrees. Find the two equal base angles. (Answer: inside angle Y = 180 − 140 = 40, so each base angle = (180 − 40) ÷ 2 = 70 degrees.) A parallelogram has base 9 and height 5. One slanted side is 6. What is its area? Answer: 45. A shape is a 12 by 5 rectangle with a right triangle on top whose legs are 12 and 6. What is the total area? Answer: 96. Six Minutes @SixMinuteClass: One technique, about six minutes. The narrator's voice is synthetic (computer-generated). Independent educational video. Not affiliated with or endorsed by Math Kangaroo in USA. © 2026 Six Minutes · @SixMinuteClass