Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up Solve. 1. x + 30 = 90 2. 103 + x = 180 x = 60 3. 32 + x = 180

Problem of the Day Mrs. Meyer’s class is having a pizza party. Half the class wants pepperoni on the pizza, of the class wants sausage on the pizza, and the rest want only cheese on the pizza. What fraction of Mrs. Meyer’s class wants just cheese on the pizza? 1 3 1 6

Learn to classify angles and find their measures.

Vocabulary angle adjacent angles right angle supplementary angles acute angle complementary angles obtuse angle straight angle vertical angles congruent angles

An angle () is formed by two rays, or sides, with a common endpoint called the vertex. You can name an angle several ways: by its vertex, by its vertex and a point on each ray, or by a number. When three points are used, the middle point must be the vertex.

Additional Example 1: Classifying Angles Use the diagram to name each figure. A. two acute angles TQP, RQS mTQP = 43°; mRQS = 47° B. two obtuse angles SQP, RQT mSQP= 133°; mRQT = 137°

Additional Example 1: Classifying Angles Use the diagram to name each figure. C. a pair of complementary angles TQP, RQS mTQP + mRQS = 43° + 47° = 90 B. two pairs of supplementary angles TQP, TQR mTQP + mTQR = 43° + 137° = 180 SQP, SQR mSQP + mSQR = 133° + 47° = 180

Check It Out: Example 1 Use the diagram to name each figure. A. two acute angles AEB, CED mAEB = 15°; mCED = 75° B. two obtuse angles AEC, BED mAEC= 105°; mBED = 165°

Use the diagram to name each figure. Check It Out: Example 1 Use the diagram to name each figure. C. a pair of complementary angles AEB, CED mAEB + mCED= 15° + 75° = 90 D. a pair of supplementary angles CED, AEC mCED + mAEC = 75° + 105° = 180

Additional Example 2A: Finding Angle Measures Use the diagram to find each angle measure. If m1 = 37°, find m2. m1 + m2 = 180° 1 and 2 are supplementary. 37° + m2= 180° Substitute 37 for m1. –37° –37° Subtract 37 from both sides. m2 = 143°

Additional Example 2B: Finding Angle Measures Use the diagram to find each angle measure. Find m3 = 37°. m2 + m3 = 180° 2 and 3 are supplementary. 143° + m3 = 180° Substitute 143 for m2. –143° –143° Subtract 143 from both sides. m3 = 37°

Use the diagram to find each angle measure. Check It Out: Example 2 Use the diagram to find each angle measure. If m1 = 42°, find m2. m1 + m2 = 180° 1 and 2 are supplementary. 42° + m2= 180° Substitute 42 for m1. –42° –42° Subtract 42 from both sides. m2 = 138°

Adjacent angles have a common vertex and a common side, but no common interior points. Angles 1 and 2 in the diagram are adjacent angles. Congruent angles have the same measure. Vertical angles are the nonadjacent angles formed by two intersecting lines. Angles 2 and 4 are vertical angles. Vertical angles are congruent.

Additional Example 3: Application A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 1: Find mCBD. ABF  CBD Vertical angles are congruent. Congruent angles have the same measure. mABF = mCBD mCBD = 26 Substitute 26 for mCBD.

Additional Example 3 Continued A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. Step 2: Find mDBE. mCBD + mDEB = 90° The angles are complementary. 26 + mDEB = 90° Substitute 26 for mCBD. –26° –26° Subtract 26 from both sides. mDEB = 64°

Check It Out: Example 3 A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. 19 Step 1: Find mCBD. ABF  CBD Vertical angles are congruent. Congruent angles have the same measure. mABF = mCBD mCBD = 19 Substitute 19 for mCBD.

Check It Out: Example 3 Continued A traffic engineer designed a section of roadway where three streets intersect. Based on the diagram, what is the measure of DBE. 19 Step 2: Find mDBE. mCBD + mDEB = 90° The angles are complementary. 19 + mDEB = 90° Substitute 19 for mCBD. –19° –19° Subtract 19 from both sides. mDEB = 71°

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 20

Lesson Quiz Use the diagram to name each figure or find each angle measure. 1. a right angle Possible answer: CGD 2. two acute angles Possible answer: 1, 2 3. pair of complementary angles Possible answer: 3, 4 4. If m1 = 47°, then find m 3. 47° 5. Find m4. 43°

Lesson Quiz for Student Response Systems 1. If m1 = 42°, then find m 3. A. 3° B. 42° C. 48° D. 90° 22

Lesson Quiz for Student Response Systems 2. Name a pair of complementary angles. A. CGD B. AGF C. AGB, BGC D. CGD, DGF 23

Lesson Quiz for Student Response Systems 3. Find mCGD. A. 3° B. 42° C. 90° D. 180° 24