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Measuring and 1-3 Constructing Angles Warm Up Lesson Presentation
Lesson Quiz Holt McDougal Geometry Holt Geometry
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Objectives Name and classify angles.
Measure and construct angles and angle bisectors.
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Example 1: Naming Angles
A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. Possible answer: BAC CAD BAD
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Example 2: Measuring and Classifying Angles
Find the measure of each angle. Then classify each as acute, right, or obtuse. A. WXV mWXV = 30° WXV is acute. B. ZXW mZXW = |130° - 30°| = 100° ZXW = is obtuse.
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Example 3: Using the Angle Addition Postulate
mDEG = 115°, and mDEF = 48°. Find mFEG mDEG = mDEF + mFEG Add. Post. 115 = 48 + mFEG Substitute the given values. –48° –48° Subtract 48 from both sides. 67 = mFEG Simplify.
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An angle bisector is a ray that divides an angle into two congruent angles.
JK bisects LJM; thus LJK KJM.
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Example 4: Finding the Measure of an Angle
KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.
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Example 4 Continued Step 1 Find x. mJKM = mMKL Def. of bisector (4x + 6)° = (7x – 12)° Substitute the given values. Add 12 to both sides. 4x = 7x Simplify. –4x –4x Subtract 4x from both sides. 18 = 3x Divide both sides by 3. 6 = x Simplify.
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Example 4 Continued Step 2 Find mJKM. mJKM = 4x + 6 = 4(6) + 6 Substitute 6 for x. = 30 Simplify.
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Check It Out! Example 4a Find the measure of each angle. QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS. Step 1 Find y. Def. of bisector Substitute the given values. 5y – 1 = 4y + 6 Simplify. y – 1 = 6 Subtract 4y from both sides. y = 7 Add 1 to both sides.
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Check It Out! Example 4a Continued
Step 2 Find mPQS. mPQS = 5y – 1 = 5(7) – 1 Substitute 7 for y. = 34 Simplify.
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Check It Out! Example 4b Find the measure of each angle. JK bisects LJM, mLJK = (-10x + 3)°, and mKJM = (–x + 21)°. Find mLJM. Step 1 Find x. LJK = KJM Def. of bisector (–10x + 3)° = (–x + 21)° Substitute the given values. +x x Add x to both sides. Simplify. –9x + 3 = 21 –3 –3 Subtract 3 from both sides. –9x = 18 Divide both sides by –9. x = –2 Simplify.
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Check It Out! Example 4b Continued
Step 2 Find mLJM. mLJM = mLJK + mKJM = (–10x + 3)° + (–x + 21)° = –10(–2) + 3 – (–2) + 21 Substitute –2 for x. = Simplify. = 46°
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Lesson Quiz: Part I Classify each angle as acute, right, or obtuse. 1. XTS acute 2. WTU right 3. K is in the interior of LMN, mLMK =52°, and mKMN = 12°. Find mLMN. 64°
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Lesson Quiz: Part II 4. BD bisects ABC, mABD = , and mDBC = (y + 4)°. Find mABC. 32° 5. Use a protractor to draw an angle with a measure of 165°.
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Lesson Quiz: Part III 6. mWYZ = (2x – 5)° and mXYW = (3x + 10)°. Find the value of x. 35
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