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1. Use the figure below to find the following:

[Please refer to the attachment for the figure and problem details]

2. Angle PQR and Angle ABC are supplementary angles and Angle PQR is nine times as large as Angle ABC. Determine the measure of each angle.

3. What is the exact area of a circle with a diameter of 11 inches?

4. The following triangles, Angle ABC and Angle DEF, are congruent.

[Please refer to the attachment for the figure]

Find the lengths of all missing sides and measures of all angles for both triangles. Include correct units with each of your answers.

First triangle: Second triangle:

Side AB = Side DF =
Angle BAC = Side EF =
Angle ABC =
Angle DEF =
Angle EFD =

5. Find the area of a trapezoid with a height of 4 m and bases of 13 m and 22 m.

6. A recreation room has the following dimensions. Carpeting will cost \$1.50 a square foot. How many square feet of carpet will be needed and how much will it cost? Include correct units at each stage within your solution.

7. Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the longest side is 52 mm. Include correct units with each part of your solution

8. How many cubic centimeters can a cigar box hold if its dimensions are 4 centimeters by 13 centimeters by 8 centimeters? Include correct units with your solution.

9. An ice cube that measures 2.4 centimeters on each side contains how many cubic centimeters of ice? Include correct units with your solution.

10. Find the approximate value of the volume of the right circular cone with a circular base shown below. Approximate your solution to the nearest hundredth.

[Please refer to the attachment for the figure]

11. In a 9 inch square cake pan and a 10 inch square cake pan, what is the difference in volume each pan will hold? Assume each pan is 2 inches high. Show step by step work. Include correct units with your solution.

12. For the following floor plan, determine whether it is possible for a person to walk through each doorway without using any of the doorways twice. If it is possible, state such a path. If it is not possible, answer, "not possible."

[Please refer to the attachment for the figure]

https://brainmass.com/math/triangles/geometry-supplementary-angles-360306

## SOLUTION This solution is FREE courtesy of BrainMass!

(FB) âƒ¡
Point F and C.
âˆ†BCF

Let âˆ ABC=x. According to the given condition âˆ PQR=9x.
They are supplementary angles.
âˆ ABC+âˆ PQR=180Â°
Or,x+9x=180Â°
Or,10x=180Â°
Or,x=(180Â°)/10=18Â°
Thus,âˆ ABC=x=18Â°
âˆ PQR=9x=9Ã—18Â°=162Â°

The diameter of the circle is 11 inches.
Radius of the circle = d/2=5.5 inches.
Area of the circle is given as
Area=Ï€r^2=Ï€(5.5)^2=30.25Ï€ sq.inch.

First Triangle Second Triangle
AB = 48 cm DF = 52 cm
Angle BAC = 23Â° EF = 20 cm
Angle ABC = 90Â° Angle DEF = 90Â°
Angle EFD = 67Â°

Area of the trapezoid is given as
Area=1/2Ã—4m Ã—(13+22)m=70 m^2

Total area of the recreation room = Area of the rectangle + Area of the triangle + Area of the square.
Total Area={(12Ã—30) +(1/2Ã—12Ã—8)+(8^2 )}sq.ft

={ 360+48+64}sq.ft
=472 sq.ft
Thus, 472 sq. ft. of carpet will be needed.
Carpeting cost is \$1.50 per square feet.
Total Cost of Carpeting =\$1.50Ã—472=\$708

Let the third side of the triangle be x.
In a right angles triangle, the hypotenuse is the longest side.
According to Pythagoras Theorem,
x^2+ã€–20ã€—^2 mm^2=ã€–52ã€—^2 mm^2

Or,x^2=ã€–(52ã€—^2-ã€–20ã€—^2)mm^2=2304 mm^2

Or,x=âˆš({2304 mm^2 } )=48 mm

Thus the third side of the triangle is 48 mm.
Perimeter of the triangle =(48+20+52)mm=120 mm
Area of the triangle=1/2Ã—48mmÃ—20mm=480 mm^2

The cigar box can hold cubic centimeters equal to its own volume.
Volume=4cmÃ—13cmÃ—8cm=416 cm^3
Thus, the cigar box can hold 416 cubic centimeters.

Volume=(2.4cm)^3=13.824 cm^3
The ice cube contains 13.824 cubic centimeters of ice.

The radius of the circular base is given as follows:
We shall calculate the altitude of the right circular cone by using Pythagoras Theorem.

Altitude^2=(50m)^2-(14m)^2=2304 m^2

Altitude=âˆš(2304 m^2 )=48m
The volume of the right circular cone is given as follows:
Volume=1/3 Ï€r^2 h=1/3Ã—3.14Ã—(14m)^2Ã—48m=9847.04m^2

The volume of the 9 inch square pan is given as 9 inchÃ—9 inchÃ—2 inch=162 cubic inch
The volume of the 10 inch square pan is given as 10 inchÃ—10 inchÃ—2 inch=200 cubic inch
The difference in volumes = 200cubic inch-162 cubic inch=38 cubic inch

'Not possible'.
The given network has only one odd vertex (B) and hence it is not traversable.

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