Understanding Angles, Areas, and Volumes in Geometry

Angles of a Triangle A B C The three angles of a triangle have a sum equal to 180 degrees. A + B + C = 180

Example A triangle has three angles , A , B and C. Angle B is 10 less than two times angle A. Angle C is 10 more than three times angle A. Find the measure of each angle.

Supplementary Angles Angles A and B have a sum of 180 degrees. A + B = 180 A = 180 – B B = 180 - A A B

Complementary Angles Angles A and B have a sum of 90 degrees. A + B = 90 A = 90 - B B A

Example Find the angle such that its supplement added with its complement equals 230 degrees.

Rectangles L W Area = (Length)(Width) = LW Perimeter = 2W + 2L Note: These formulas are just algebraic expressions. If we know the values for the variables, then we can Evaluate the area and perimeter.

Example 7 ft 3ft Find the area and perimeter. A = LW = (7)(3) = 21ft² P = 2W + 2L = 2(3) + 2(7) = 6 +14 = 20 ft

Perimeter 16 m W Find the width if the perimeter is 56 meters.

Triangles Height=h Base = b Area = bh

Triangle Area =48 cm² 12cm Find the height , h

Circles Radius = r Area = r² Circumference = 2 r

Circles 4 meters Find the approximate area and circumference.

Swimming Pool 20ft 14ft 7ft 5ft

Volume of a Rectangular Solid L W H Volume = LWH

Volume of a Sphere Radius=r Find the volume if the radius = 3 meters

Vertical Angles are formed when two lines are intersected. A C B D Angle A = Angle D and Angle C = Angle B

Find the measure of each Angle (10x+15) (12x-3)

Find the measure of each angle (3x +10) (5x+10)

Solving Formulas for one variable If C = 25, find F Solve the formula for C If F = 82, find C

Solve each formula for the stated variable. a) • P = 2W + 2L , for W • Ax + By = C , for y • A = p + prt , for r For b

Understanding Angles, Areas, and Volumes in Geometry