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4-2 Angles of Triangles

You classified triangles by their side or angle measures. 4-2 Angles of Triangles. Apply the Triangle Angle-Sum Theorem. Apply the Exterior Angle Theorem. The Three Angles. Number the angles of your triangle. Fold the top angle (1) to touch the opposite side.

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4-2 Angles of Triangles

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  1. You classified triangles by their side or angle measures. 4-2 Angles of Triangles • Apply the Triangle Angle-Sum Theorem. • Apply the Exterior Angle Theorem.

  2. The Three Angles • Number the angles of your triangle. • Fold the top angle (1) to touch the opposite side. • Fold the side angles (2 & 3) to meet angle 1. • What do you notice?

  3. Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180°

  4. Page 246

  5. Try It Two angles of a triangle measure 40° and 58°. What is the measure of the third angle? 82° ? 58° 40°

  6. SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. Understand Examine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that 1 and 2 are vertical angles.

  7. Plan Find m1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m2. Then you will have enough information to find the measure of 3. Solve Triangle Angle-Sum Theorem Simplify. Subtract 117 from each side.

  8. 1 and 2 are congruent vertical angles. So, m2 = 63. Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side. Answer:Therefore, m1 = 63, m2 = 63, and m3 = 38. Check The sums of the measures of the angles in each triangle should be 180.m1 + 43 + 74 = 63 + 43 + 74 or 180m2 + m3 + 79 = 63 + 38 + 79 or 180

  9. Find the measure of 3. A. 95 B. 75 C. 57 D. 85

  10. Exterior Angle An exterior angle is formed by extending one of the side of the triangle. Exterior angle

  11. Adjacent Interior Angle… The interior angle in a linear pair with an exterior angle. An exterior angle Adjacent interior angle

  12. Remote Interior Angles The two angles that are away from the exterior angle. Remote interior angle Exterior angle Remote interior angle

  13. GARDENING Find the measure of FLW in the fenced flower garden shown. mLOW + mOWL = mFLW Exterior Angle Theorem x + 32 = 2x – 48 Substitution 32 = x – 48 Subtract x from each side. 80 = xAdd 48 to each side. Answer: So, mFLW = 2(80) – 48 or 112.

  14. m1 = 48 + 56 Exterior Angle Theorem = 104 Simplify. If 2 s form a linear pair, they are supplementary. 104 + m2 = 180 Substitution 76 Subtract 104 from each side. Find the measure of each numbered angle.

  15. m 3 = 90 – 48 If 2 s form a right angle, they are complementary. = 42 Simplify. Triangle Angle-Sum Theorem (90 – 34) + m2+ m 4 = 180 56 + 76 + m 4 = 180 Substitution Simplify. 132 + m4 = 180 48 Subtract 132 from each side.

  16. m5 + 41 + 90 = 180 Triangle Angle-Sum Theorem m5 + 143 = 180 Simplify. 49 Subtract 131 from each side. m1 = 104,m2 = 76, m3 = 42,m4 = 48, m5 = 49

  17. What is a triangle? A figure formed by three line segments that connect three noncollinear points. • What is the sum of the measures of the interior of any triangle? The sum of the measures of the angles of a triangle is 180° • How are triangles classified and named? Triangles are classified by sides and angles. Sides: scalene, isosceles and equilateral. Angles: acute, obtuse, right and equiangular.

  18. 4-2 Assignment Page 250, 12 – 27 Skip 16 Show how you got your answer (180 - ? - ? = answer)

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