Measuring and Constructing Angles 1 3 Constructing Angles

Measuring and Constructing Angles 1 -3 Constructing Angles Warm Up Lesson Presentation Lesson Quiz Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Objectives Name and classify angles. Measure and construct angles and angle bisectors. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles 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 Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 2: Measuring and Classifying Angles Find the measure of each angle. Then classify each as acute, right, or obtuse. A. WXV m WXV = 30° WXV is acute. B. ZXW m ZXW = |130° - 30°| = 100° ZXW = is obtuse. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 3: Using the Angle Addition Postulate m DEG = 115°, and m DEF = 48°. Find m FEG m DEG = m DEF + m FEG Add. Post. 115 = 48 + m FEG Substitute the given values. – 48° Subtract 48 from both sides. 67 = m FEG Simplify. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles An angle bisector is a ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK KJM. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 4: Finding the Measure of an Angle KM bisects JKL, m JKM = (4 x + 6)°, and m MKL = (7 x – 12)°. Find m JKM. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Example 4 Continued Step 1 Find x. m JKM = m MKL Def. of bisector (4 x + 6)° = (7 x – 12)° +12 Substitute the given values. 4 x + 18 – 4 x = 7 x – 4 x 18 = 3 x 6=x Holt Mc. Dougal Geometry Add 12 to both sides. Simplify. Subtract 4 x from both sides. Divide both sides by 3. Simplify.

1 -3 Measuring and Constructing Angles Example 4 Continued Step 2 Find m JKM = 4 x + 6 = 4(6) + 6 Substitute 6 for x. = 30 Simplify. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Check It Out! Example 4 a Find the measure of each angle. QS bisects PQR, m PQS = (5 y – 1)°, and m PQR = (8 y + 12)°. Find m PQS. Step 1 Find y. Def. of bisector Substitute the given values. 5 y – 1 = 4 y + 6 y– 1=6 y=7 Holt Mc. Dougal Geometry Simplify. Subtract 4 y from both sides. Add 1 to both sides.

1 -3 Measuring and Constructing Angles Check It Out! Example 4 a Continued Step 2 Find m PQS = 5 y – 1 = 5(7) – 1 Substitute 7 for y. = 34 Simplify. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Check It Out! Example 4 b Find the measure of each angle. JK bisects LJM, m LJK = (-10 x + 3)°, and m KJM = (–x + 21)°. Find m LJM. Step 1 Find x. LJK = KJM (– 10 x + 3)° = (–x + 21)° +x +x – 9 x + 3 = 21 – 3 – 9 x = 18 x = – 2 Holt Mc. Dougal Geometry Def. of bisector Substitute the given values. Add x to both sides. Simplify. Subtract 3 from both sides. Divide both sides by – 9. Simplify.

1 -3 Measuring and Constructing Angles Check It Out! Example 4 b Continued Step 2 Find m LJM = m LJK + m KJM = (– 10 x + 3)° + (–x + 21)° = – 10(– 2) + 3 – (– 2) + 21 Substitute – 2 for x. = 20 + 3 + 21 = 46° Holt Mc. Dougal Geometry Simplify.

1 -3 Measuring and Constructing Angles 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, m LMK =52°, and m KMN = 12°. Find m LMN. 64° Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Lesson Quiz: Part II 4. BD bisects ABC, m ABD = , and m DBC = (y + 4)°. Find m ABC. 32° 5. Use a protractor to draw an angle with a measure of 165°. Holt Mc. Dougal Geometry

1 -3 Measuring and Constructing Angles Lesson Quiz: Part III 6. m WYZ = (2 x – 5)° and m XYW = (3 x + 10)°. Find the value of x. 35 Holt Mc. Dougal Geometry