7-3 Angles in Triangles Warm Up Problem of the Day Lesson Presentation Course 3

7-3 Angles in Triangles Warm Up Solve each equation. Course 3 7-3 Angles in Triangles Warm Up Solve each equation. 1. 62 + x + 37 = 180 2. x + 90 + 11 = 180 3. 2x + 18 = 180 4. 180 = 2x + 72 + x x = 81 x = 79 x = 81 x = 36

7-3 Angles in Triangles Problem of the Day Course 3 7-3 Angles in Triangles Problem of the Day What is the one hundred fiftieth day of a non-leap year? May 30

7-3 Angles in Triangles Learn to find unknown angles in triangles. Course 3 7-3 Angles in Triangles Learn to find unknown angles in triangles.

Insert Lesson Title Here Course 3 7-3 Angles in Triangles Insert Lesson Title Here Vocabulary Triangle Sum Theorem acute triangle right triangle obtuse triangle equilateral triangle isosceles triangle scalene triangle

Course 3 7-3 Angles in Triangles If you tear off two corners of a triangle and place them next to the third corner, the three angles seem to form a straight line.

Course 3 7-3 Angles in Triangles Draw a triangle and extend one side. Then draw a line parallel to the extended side, as shown. The sides of the triangle are transversals to the parallel lines. The three angles in the triangle can be arranged to form a straight line or 180°.

Course 3 7-3 Angles in Triangles An acute triangle has 3 acute angles. A right triangle has 1 right angle. An obtuse triangle has 1 obtuse angle.

Course 3 7-3 Angles in Triangles Additional Example 1A: Finding Angles in Acute, Right and Obtuse Triangles Find p° in the acute triangle. 73° + 44° + p° = 180° 117° + p° = 180° –117° –117° p° = 63°

Course 3 7-3 Angles in Triangles Additional Example 1B: Finding Angles in Acute, Right, and Obtuse Triangles Find c° in the right triangle. 42° + 90° + c° = 180° 132° + c° = 180° –132° –132° c° = 48°

Course 3 7-3 Angles in Triangles Additional Example 1C: Finding Angles in Acute, Right, and Obtuse Triangles Find m° in the obtuse triangle. 23° + 62° + m° = 180° 85° + m° = 180° –85° –85° m° = 95°

7-3 Angles in Triangles Check It Out: Example 1A Course 3 7-3 Angles in Triangles Check It Out: Example 1A Find a° in the acute triangle. 88° + 38° + a° = 180° 38° 126° + a° = 180° –126° –126° a° = 54° a° 88°

7-3 Angles in Triangles Check It Out: Example 1B Course 3 7-3 Angles in Triangles Check It Out: Example 1B Find b in the right triangle. 38° 38° + 90° + b° = 180° 128° + b° = 180° –128° –128° b° = 52° b°

7-3 Angles in Triangles Check It Out: Example 1C Course 3 7-3 Angles in Triangles Check It Out: Example 1C Find c° in the obtuse triangle. 24° + 38° + c° = 180° 38° 62° + c° = 180° 24° c° –62° –62° c° = 118°

Course 3 7-3 Angles in Triangles An equilateral triangle has 3 congruent sides and 3 congruent angles. An isosceles triangle has at least 2 congruent sides and 2 congruent angles. A scalene triangle has no congruent sides and no congruent angles.

Course 3 7-3 Angles in Triangles Additional Example 2A: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find the angle measures in the equilateral triangle. 3b° = 180° Triangle Sum Theorem 3b° 180° 3 3 = Divide both sides by 3. b° = 60° All three angles measure 60°.

Course 3 7-3 Angles in Triangles Additional Example 2B: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find the angle measures in the isosceles triangle. 62° + t° + t° = 180° Triangle Sum Theorem 62° + 2t° = 180° Combine like terms. –62° –62° Subtract 62° from both sides. 2t° = 118° 2t° = 118° 2 2 Divide both sides by 2. t° = 59° The angles labeled t° measure 59°.

Course 3 7-3 Angles in Triangles Additional Example 2C: Finding Angles in Equilateral, Isosceles, and Scalene Triangles Find the angle measures in the scalene triangle. 2x° + 3x° + 5x° = 180° Triangle Sum Theorem 10x° = 180° Combine like terms. 10 10 Divide both sides by 10. x = 18° The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

7-3 Angles in Triangles Check It Out: Example 2A Course 3 7-3 Angles in Triangles Check It Out: Example 2A Find the angle measures in the isosceles triangle. 39° + t° + t° = 180° Triangle Sum Theorem 39° + 2t° = 180° Combine like terms. –39° –39° Subtract 39° from both sides. 2t° = 141° 2t° = 141° 2 2 Divide both sides by 2 39° t° = 70.5° t° The angles labeled t° measure 70.5°. t°

7-3 Angles in Triangles Check It Out: Example 2B Course 3 7-3 Angles in Triangles Check It Out: Example 2B Find the angle measures in the scalene triangle. 3x° + 7x° + 10x° = 180° Triangle Sum Theorem 20x° = 180° Combine like terms. 20 20 Divide both sides by 20. x = 9° 10x° The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°. 3x° 7x°

7-3 Angles in Triangles Check It Out: Example 2C Course 3 7-3 Angles in Triangles Check It Out: Example 2C Find the angle measures in the equilateral triangle. 3x° = 180° Triangle Sum Theorem 3x° 180° 3 3 = x° x° = 60° x° x° All three angles measure 60°.

Course 3 7-3 Angles in Triangles Additional Example 3: Finding Angles in a Triangle that Meets Given Conditions The second angle in a triangle is six times as large as the first. The third angle is half as large as the second. Find the angle measures and draw a possible picture. Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle measure. 12

Additional Example 3 Continued Course 3 7-3 Angles in Triangles Additional Example 3 Continued Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 12 x° + 6x° + 3x° = 180° Triangle Sum Theorem 10x° = 180° Combine like terms. 10 10 Divide both sides by 10. x° = 18°

Additional Example 3 Continued Course 3 7-3 Angles in Triangles Additional Example 3 Continued Let x° = the first angle measure. Then 6x° = second angle measure, and (6x°) = 3x° = third angle. 12 x° = 18° The angles measure 18°, 54°, and 108°. The triangle is an obtuse scalene triangle. 3 • 18° = 54° 6 • 18° = 108° X° = 18°

7-3 Angles in Triangles Check It Out: Example 3 Course 3 7-3 Angles in Triangles Check It Out: Example 3 The second angle in a triangle is three times larger than the first. The third angle is one third as large as the second. Find the angle measures and draw a possible picture. Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle measures. 13

Check It Out: Example 3 Continued Course 3 7-3 Angles in Triangles Check It Out: Example 3 Continued Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = 3x° = third angle. 13 x° + 3x° + x° = 180° Triangle Sum Theorem 5x° = 180° Combine like terms. 5 5 Divide both sides by 5. x° = 36°

Check It Out: Example 3 Continued Course 3 7-3 Angles in Triangles Check It Out: Example 3 Continued Let x° = the first angle measure. Then 3x° = second angle measure, and (3x°) = x° = third angle. 13 The angles measure 36°, 36°, and 108°. The triangle is an obtuse isosceles triangle. x° = 36° 3 • 36° = 108° x° = 36° 36° 108°

7-3 Angles in Triangles Lesson Quiz: Part I Course 3 7-3 Angles in Triangles Lesson Quiz: Part I 1. Find the missing angle measure in the acute triangle shown. 38° 2. Find the missing angle measure in the right triangle shown. 55°

7-3 Angles in Triangles Lesson Quiz: Part II Course 3 7-3 Angles in Triangles Lesson Quiz: Part II 3. Find the missing angle measure in an acute triangle with angle measures of 67° and 63°. 50° 4. Find the missing angle measure in an obtuse triangle with angle measures of 10° and 15°. 155°