Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° 105° 67° 40° 35° 35 105 40 180 33° 90 67 33 180 Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° 105° 67° 40° 35° 35 105 40 180 33° 90 67 33 180 So given a triangle, and any two angles, you could find the third angle. Triangles and Lines – Sum of the Angles in a Triangle The sum of the angles in any triangle = 180° 105° 67° 40° 35° 33° 35 105 40 180 90 67 33 180 So given a triangle, and any two angles, you could find the third angle. missing angle 180 1 2 Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 1 : Find the missing angle in the triangle. x 48° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 1 : Find the missing angle in the triangle. missing angle 180 1 2 x missing angle 180 90 48 missing angle 180 138 missing angle 42 48° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 2 : Find the missing angle in the triangle. 15° x 28° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 2 : Find the missing angle in the triangle. missing angle 180 1 2 missing angle 180 15 28 missing angle 180 43 missing angle 137 15° x 28° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 3 : Find the missing angle in the triangle. x 70° 150° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 3 : Find the missing angle in the triangle. x 70° ? 150° We must first find the supplementary angle for this linear pair… Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 3 : Find the missing angle in the triangle. x 70° ? 150° We must first find the supplementary angle for this linear pair… 180 150 30 Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 3 : Find the missing angle in the triangle. missing angle 180 1 2 x 70° missing angle 180 70 30 missing angle 180 100 missing angle 80 30° 150° We must first find the supplementary angle for this linear pair… 180 150 30 Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 4 : Find the missing angle. 92° x 56° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 4 : Find the missing angle. missing angle 180 92 56 92° missing angle 180 148 missing angle 32 32° x 56° First find the missing angle in the triangle… Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 4 : Find the missing angle. missing angle 180 92 56 92° missing angle 180 148 missing angle 32 32° x 56° These are a linear pair so 180°- 32° = 148° … Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 4 : Find the missing angle. missing angle 180 92 56 92° missing angle 180 148 missing angle 32 Do you see it ? 32° 56° 148° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 4 : Find the missing angle. missing angle 180 92 56 92° missing angle 180 148 missing angle 32 Do you see it ? 32° 148° 56° Theorem – the measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles. Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 5 : Find the missing angle. x 39° 115° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 5 : Find the missing angle. x 39 115 x 154 x 39° 115° Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 6 : Find the missing angle. 51° 85° x Triangles and Lines – Sum of the Angles in a Triangle missing angle 180 1 2 EXAMPLE # 6 : Find the missing angle. 85 51 x 34 x 51° 85° Theorem – the measure of an exterior angle of a triangle is equal to the sum of the opposite interior angles. x