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Triangles: Angle Sum & Classifying Triangles Tutorial 12b The Triangle Angle-Sum Theorem The interior angles of any triangle have a sum of 180. mA + mB + mC = 180 A B C Example Problems: Find the missing angles. x =180 – (117 + 33) =30 117 x 33 z y w t 30 45 t = 60 y = 88 w = 60 z = 92 47 Exterior Angles of a Triangle An exterior angle of a polygon is an angle formed by a side and an extension of a side. For each exterior angle of a triangle, the two non-adjacent interior angles are called its remote interior angles. 1 Remote Interior Angles are 2 and 3 3 1 Exterior Angle is 2 Exterior Angle Theorem The measure of an exterior angle of a triangle equals the sum of the measures of its two remote interior angles. m1 = m2 + m3 2 1 3 Corollary: Exterior Angle Theorem The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. m1 > m2 and m1 > m3 2 1 3 Classifying Triangles: Equilateral All sides congruent By Side Lengths Isosceles At least two sides congruent Scalene No sides congruent Classifying Triangles: By Angle Measure Acute Equiangular All angles acute All angles congruent Obtuse Right One obtuse angle One right angle If you cannot remember the types of angles click here. Review A little more about Right Triangles • In a right triangle, the side opposite the right angle is the longest side. It is the called the hypotenuse. • The other two sides are called the legs of a right triangle. Side c is the hypotenuse, a c b and is the longest side. Sides a and b are the legs of the triangle. Classifying Angles Back Types of Angles: Acute Angle: Angles less than 90° are called Acute Angles. Right Angle: Obtuse Angle: Angles greater than 90° are called Obtuse Angles. Straight Angle: Symbol for right angle 180° Angles equal to 90° are called Right Angles. Angles equal to 180° are called Straight Angles.