1. § 3.3 Geometric Problems

2. Angel, Elementary Algebra, 7ed 2 Solving Geometric Problems Two angles are complementary angles if the sum of their measures is 90º. Two angles are supplementary angles if the sum of their measures is 180º. When two lines cross, the opposite angles are called vertical angles.

3. Angel, Elementary Algebra, 7ed 3 Solving Geometric Problems Example: Angle A and angle B are complementary angles, and angle A is 21º more than twice angle B. Find the measure of both angles. measure of angle A + measure of angle B = 90 Let a = angle A a = 21 + 2 (measure of angle B) a = 21 + 2 (90 - a) Solve the equation. B A Continued.

4. Angel, Elementary Algebra, 7ed 4 Solving Geometric Problems a = 21 + 2 (90 - a) a = 21 + 180 - 2a a = 201 - 2a 3a = 201 a = 67 Check: 67 + 23 = 90 The measure of angle A is 67º. The measure of angle B is 90 – 67 = 23º. Example continued:

5. Angel, Elementary Algebra, 7ed 5 Solving Geometric Problems Example: Mrs. O’Conner is planning to build a sandbox for her daughter. She has 26 feet of lumber with which to build the perimeter. What should be the dimensions of the rectangular sandbox if the length is to be 3 feet longer than the width. Let w = the width of the sandbox; length = 3 + w perimeter = 2l + 2w 26 = 2(3 + w) + 2w Solve the equation. Continued.

6. Angel, Elementary Algebra, 7ed 6 Solving Geometric Problems 26 = 2(3 + w) + 2w 26 = 6 + 2w + 2w 26 = 6 + 4w 20 = 4w 5 = w The width is 5 feet. The length = 3 + w = 3 + 5 = 8 feet Check: 2(3 + w) + 2w = 2(3 + 5) + 2(5) = 2(8) + 10 = 16 + 10 = 26 Example continued: