Measure and Classify Angles

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1.4 Measure and Classify Angles

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Presentation transcript:

Measure and Classify Angles 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.

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

Classifying Angles

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

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

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

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

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

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

GUIDED PRACTICE Use the diagram shown below. Identify all pairs of congruent angles in the diagram. In the diagram, Find the other angle measures in the diagram. SOLUTION A. There are two pairs of Congruent angles in the diagram. T S and P Q ~ B. mQPR = 84 and mPTS = 121.

Angle Bisector A line which cuts an angle into two equal halves A 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.

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

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

Example 4