AMSCO'S Geometry. New York - Rye High School

The Sum of the Measures of the Angles of a Triangle 351ExercisesWriting About Mathematics1. McKenzie said that if a triangle is obtuse, two of the angles of the triangle are acute. Do youagree with McKenzie? Explain why or why not.2. Giovanni said that since the sum of the measures of the angles of a triangle is 180, theangles of a triangle are supplementary. Do you agree with Giovanni? Explain why or whynot.Developing SkillsIn 3–6, determine whether the given numbers can be the degree measures of the angles of a triangle.3. 25, 100, 55 4. 95, 40, 45 5. 75, 75, 40 6. 12, 94, 74In 7–10, the given numbers are the degree measures of two angles of a triangle. Find the measure ofthe third angle.7. 80, 60 8. 45, 85 9. 90, 36 10. 65, 65In 11–14, the measure of the vertex angle of an isosceles triangle is given. Find the measure of a baseangle.11. 20 12. 90 13. 76 14. 110In 15–18, the measure of a base angle of an isosceles triangle is given. Find the measure of the vertexangle.15. 80 16. 20 17. 45 18. 6319. What is the measure of each exterior angle of an equilateral triangle?In 20–23, the diagram shows ABC and exterior ACD.20. If mA 40 and mB 20, find mACD andmACB.21. If mA 40 and mB 50, find mACD andmACB.22. If mA 40 and mACB 120, find mACD andmB.23. If mA 40, mB 3x 20, and mACD 5x 10,find mB,mACD, and mACB.Applying SkillsADCB24. The measure of each base angle of an isosceles triangle is 21° more than the measure of thevertex angle. Find the measure of each angle of the triangle.