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1.4 Lesson

1.4 Lesson. Measure and Classify Angles. Angle, Vertex, and Sides. an angle consists of two rays that share the same endpoint. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle. Name the three angles in diagram.

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1.4 Lesson

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  1. 1.4 Lesson Measure and Classify Angles

  2. Angle, Vertex, and Sides an angle consists of two rays that share the same endpoint. The point where the rays intersect is called the vertex of the angle. The two rays are called the sides of the angle.

  3. Name the three angles in diagram. Name this one angle in 3 different ways. Naming Angles WXY, WXZ, and YXZ What always goes in the middle? The vertex of the angle

  4. Classifying Angles

  5. EXAMPLE 1 Use the diagram to find the measure of the indicated angle. Then classify the angle a. b. c. d. 55acute 125obtuse 180straight 90 right

  6. Angle Addition Postulate If D is in the interior of <ABC, then <ABD + < DBC = <ABC Adding the 2 angle together gives you the big angle

  7. o ALGEBRAGiven that m LKN =145 , find m LKM andm MKN. STEP 1 Write and solve an equation to find the value of x. mLKN = m LKM + mMKN o o o 145 = (2x + 10)+ (4x – 3) EXAMPLE 2 Find angle measures SOLUTION Angle Addition Postulate Substitute angle measures. 145 = 6x + 7 Combine like terms. 138 = 6x Subtract 7 from each side. 23 = x Divide each side by 6.

  8. STEP 2 Evaluate the given expressions when x = 23. mLKM = (2x+ 10)° = (2 23+ 10)° = 56° mMKN = (4x– 3)° = (4 23– 3)° = 89° So, m LKM = 56°and m MKN = 89°. ANSWER EXAMPLE 2 Find angle measures

  9. 3. Given that KLMis straight angle, find mKLN andm NLM. STEP 1 Write and solve an equation to find the value of x. m KLM + m NLM = 180° (10x – 5)° + (4x +3)° = 180° = 180 14x – 2 = 182 14x x = 13 GUIDED PRACTICE Find the indicated angle measures. SOLUTION Straight angle Substitute angle measures. Combine like terms. Subtract 2 from each side. Divide each side by 14.

  10. STEP 2 Evaluate the given expressions when x = 13. mKLM = (10x– 5)° = (10 13– 5)° = 125° mNLM = (4x+ 3)° = (4 13+ 3)° = 55° mKLM = 125° mNLM = 55° ANSWER GUIDED PRACTICE

  11. Angle Bisector A A line which cuts an angle into two equal halves The blue ray on the right is the angle bisector of the angle on the left. The red ray on the right is the angle bisector of the angle on the left.

  12. In the diagram at the right, YWbisects XYZ, and mXYW = 18. Find m XYZ. o By the Angle Addition Postulate, m XYZ =mXYW + m WYZ. BecauseYW bisects XYZyou know thatXYW WYZ. So, m XYW = m WYZ, and you can write M XYZ = m XYW + m WYZ = 18° + 18° = 36°. ~ EXAMPLE 3 Double an angle measure SOLUTION

  13. Example 3 In the diagram below, YW bisects , and . Find .

  14. Example 4

  15. Angles Formed by the Intersection of 2 Lines  Click Me!

  16. Linear Pair A linear pair is formed by two angles that are adjacent (share a leg) and supplementary (add up to 180°) “forms a line”

  17. Vertical Angles A pair of non-adjacent angles formed by the intersection of two straight lines “When you draw over the 2 angles it forms an X”

  18. 1 and 4 are a linear pair. 4 and 5 are also a linear pair. Identify all of the linear pairs and all of the vertical angles in the figure at the right. ANSWER 1 and 5 are vertical angles. ANSWER EXAMPLE 4 Identify angle pairs SOLUTION To find linear pairs, look for adjacent angles whose noncommon sides are opposite rays. To find vertical angles, look or angles formed by intersecting lines.

  19. Example 5 Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle.

  20. Example 6 Given that m5 = 60 and m3 = 62, use your knowledge of linear pairs and vertical angles to find the missing angles.

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