Angles of a Triangle

Angles of a Triangle

The three angles of a triangle have a sum equal to 180 degrees.

A + B + C = 180

B

A

C

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

BA

Complementary Angles

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

AB

Example

Find the angle such that its supplement

added with its complement equals 230

degrees.

RectanglesL

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.

Example7 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

Base = b

Height=h

Area = bh 21

Triangle

Area =48 cm²

12cm

Find the height , h

Circles

14.3

Radius = r

Area = r²

Circumference = 2 r

Circles

4 meters

Find the approximate area and circumference.

Swimming Pool20ft

14ft

5ft

7ft

Volume of a Rectangular Solid

LW

H

Volume = LWH

Volume of a Sphere

Radius=r

³34 rV

Find the volume if the radius = 3 meters

Vertical Angles are formed when two lines are intersected.

ABC

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

3259

CF

If C = 25, find F

Solve the formula for C

If F = 82, find C

Solve each formula for the stated variable.

a)

b) P = 2W + 2L , for W

c) Ax + By = C , for y

d) A = p + prt , for r

bHA21

For b