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4.2: Measuring Angles in Triangles

4.2: Measuring Angles in Triangles. p. 189-195. Thm 4.1:Triangle Sum Thm. The sum of the measures of the interior angles of a triangle is 180 o . m  A + m  B+ m  C=180 o + + = 180. A. B. C. Example 1. Name Triangle AWE by its angles.

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4.2: Measuring Angles in Triangles

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  1. 4.2: Measuring Angles in Triangles p. 189-195

  2. Thm 4.1:Triangle Sum Thm • The sum of the measures of the interior angles of a triangle is 180o. • mA + mB+ mC=180o + + = 180 A B C

  3. Example 1 • Name Triangle AWE by its angles mA + mW+ mE=180o (3x+5) + ( 8x+22) + (4x-12) = 180 A 15x + 15 = 180 15x = 165 x = 11 3x +5 mA = 3(11) +5 = 38o 8x + 22 mW = 8(11)+22 = 110o 4x - 12 W mE = 4(11)-12 = 32o E Triangle AWE is obtuse

  4. Example 2 Solve for x . Ans: (5x+24) + (5x+24) + (4x+6) = 180 5x +24 + 5x+ 24 + 4x+6 = 180 14x + 54 = 180 14x = 126 x = 9 5x +24

  5. Exterior Angles(formed by extending the sides) ( D E F )) ((

  6. Thm 4.2: Exterior Angles Thm • The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. • m1=mA+ mB m1= + A 1 B C

  7. Example Find every angle measure Exterior angle = 2 nonadjacent angles 65 3x-10 = (25) + (x+15) 3x-10 = x +40 2x= 50 x = 25 115 40

  8. Exterior angle example Solve for q

  9. Example Find the missing angles 80 80 60 40 50 50 70 110 110 70

  10. Example Find the measure of each numbered angle in the figure.

  11. Corollary to triangle sum thm (Corollary- a statement easily proved using a thm.) * The acute angles of a right triangle are complementary. A A is comp. to C B C

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