MAT 164 9.1-9.3 HW/QUIZ REVEIW

Lines L and M are parallel. Determine which of the lettered angles are alternate interior

angles.

<n and <u

Lines L and M are parallel. Determine which of the lettered angles are obtuse angles.

<g and <c

Lines L and M are parallel. Determine which of the lettered angles are supplementary angles to angle∠t.

<d, <u, <v, <f

Determine whether the following statement is true or false. If two equal angles are​ supplementary, then each is a right angle.

TRUE

Determine whether the following statement is true or false.

An angle cannot be the complement of one angle and the supplement of another angle at the same time.

FALSE

Assume that lines L and M are parallel. Find a pair of acute, alternate exterior angles.

angels f and y

Assume that lines L and M are parallel.Find a pair of acute​, corresponding angles.

j and r, h and q

Find the measure of the complement and the supplement of

40°.

What is the measure of the complement of

40°​?

What is the measure of the supplement of

40°​?

The complementary angle is

50°. The supplementary angle is

140°

Find the measure of the complementary angle and the supplementary angle for each angle.

131°

there is no complementary angle

The supplementary angle is

49°

Find the measure of the complement and the supplement of

44.7°.

The complementary angle is

45.3°

The supplementary angle is

135.3°

if

x=42°​,

Find the measures of angles​ 1, 2, and 3.

∠1=138°

<2=42°

∠3=138°

Find the measures of angles​ a, b, and c.

∠a=39°

∠b=51*

∠c=129°

The figure to the right shows two parallel lines intersected by more than one transversal. Let x equals 37 degrees .x=37°. Find the measure of angles​ 1, 2, and 3.

∠1=37°

∠2=53°

∠3=143°

You are given the circumference of the circle and the measure of the central angle ACB. Find the length of arc AB. circumference=36 feet;∠ACB=80​°

The length of arc AB is 8 feet.

Given the circumference of the circle and the length of arc​ AB, find the measure of the central angle ACB.circumferences=12 meters; length of arc AB=3meters

∠ACB=90°

You are given two of the following three pieces of​ information: the circumference of the​ circle, the measure of the central angle​ ACB, and the length of the arc. Find the third piece of information.

∠ACB=30°​; length of arc AB=60 centimeters

The circumference of the circle is 720 cm

Given the circumference of the circle and the measure of the central angle​ ACB, find the length of arc BD. circumference=18 ​feet;∠ACB=120°

The length of arc BD is 33 feet.

Find ∠BCD Given the information below. circumference=48 inches; length of arc DE=4nches

∠BCD=150°

Solve for x. Assume that lines L and M are parallel.

x=9°

Solve for x.

x=15°

An angle such as angle∠ABC is called an inscribed angle, and it can be proved that the measure​ (in degrees) of an inscribed angle is half the measure​ (in degrees) of the arc it cuts. So if the measure of arc AC is 60degrees°​, then the measure of angle∠ABC would be 30degrees°. Recall that∠ADC is a central angle. If ∠D=40° and the circumference of the circle is 36 inches, then what is the length of arc​ AC?

The length of arc AC is

44

​inch(es).

An angle such as

∠ABC is called an inscribed angle and it can be proved that the measure​ (in degrees) of an inscribed angle is half the measure​ (in degrees) of the arc it cuts. If the circumference of the circle is 120 Inches and the length of arc AC is 16 inches, then what is ∠​B?

∠B=24°

Two lines in a plane can intersect forming four angles​ (some may have the same​ measure). What is the greatest number of angles that can be formed using three​ lines?

Using three​ lines, 12 angles can be formed.

Find the measure of angle x to make a​ hole-in-one at the miniature golf course hole to the right. Use the following two facts to find x.

​1) The angle the ball makes as it hits a flat surface has the same measure as the angle the ball makes as it leaves the surface.

​2) The sum of the measures of the interior​ (inside) angles of a triangle totals​ 180°.

x=43°

What is the difference between supplementary and complementary​ angles?

The sum of the measures of complementary angles is 90°, while the sum of the measures of supplementary angles is 180°.

HW 9.2

Q1) A plane figure is considered​ _______ if it can be drawn without lifting the pencil and if the starting and ending points are the same. A plane figure is considered​ _______ if it can be drawn without lifting the pencil and in drawing it we never passes through the same point​ twice, with the possible exception of the starting and ending points.

CLOSED AND SIMPLE.

HW 9.2

Q2) Fill in the blanks.

A​ _______ is a​ simple, closed plane figure consisting only of line​ segments, such that no two consecutive edges lie on the same line. We call an endpoint of an edge a​ ______. A polygon is​ _______ if all of its edges are the same length and all of its angles have the same measure.

POLYGON, VERTEX AND REGULAR

HW 9.2

Q3) Fill in the blanks.

In order for to polygons to be considered​ similar, their corresponding sides must be​ _______ and their corresponding angles must be​ _______.

PROPORTIONAL AND EQUAL

HW 9.2

Q4) State whether the figure is a polygon. If it is not a​ polygon, state what part of the definition fails.

This figure is a polygon

HW 9.2

Q5)

State whether the figure is a polygon. If it is not a​ polygon, state what part of the definition fails.

This figure is a polygon

HW 9.2

Q6) The measures of the angles of the triangle are indicated in terms of x. Find the measure of angle A.

The measure of angle A is

15°.

HW 9.2

G7) The measures of the angles of the triangle are indicated in terms of x. Find the measure of angle A.

The measure of angle A is

129°.

HW 9.2

Q8)

The measures of the angles of the triangle are indicated in terms of x. Find the measure of angle A.

The measure of angle A is

84°.

HW 9.2

G9) What is the measure of an interior angle of a regular polygon with 9 ​sides?

Each angle of a regular polygon with 99 Sides measures 140°.

HW 9.2

Q10) If each interior angle of a regular polygon measures 156°​ how many sides does the polygon​ have?

The polygon has 15 sides.

HW 9.2

Q11) Given that the pair of triangles are​ similar, find the length of the side labeled x.

The length of the side labeled x is

8 inches.

HW 9.2

Q12) Question content area top

Assume that the figures shown to the right are similar. Given the lengths of sides and measures of angles in the left​ figure, what information is known about the right​ figure?

The measure of angle

E is 41°

The length of side

EH is 16

HW 9.2

Q13) Assume that the figures shown to the right are similar. Given the lengths of sides and measures of angles in the left​ figure, what information is known about the right​ figure?

The measure of angle

E is 47°.

The length of side

FG is 98

HW 9.2

Q14)

Assume that the figures shown to the right are similar. Given the lengths of sides and measures of angles in the left​ figure, what information is known about the right​ figure?

The measure of angle

I is 40*.

The length of side

HI is 77

HW 9.2

Q15) A guy wire supports an​ energy-producing windmill as shown here. If angle A is

136°​,

what is the measure of angle​ B?

The measure of angle B is

46°.

HW 9.2

Q16) Find the​ distance, d, across the river. Assume that the triangles are similar and the ratio of d to 120 ft is the same as the ratio of 250ft to 50 ft.

The distance across the river is

600 feet.

HW 9.2

Q17) If triangles ABC and ADE are similar in this​ diagram, what is the length of the​ pond?

The pond is 210 ft long.

HW 9.2

Q18)

Assume that the triangles formed by the legs of this camping cot are isosceles and that angle A is 90°.Find the measure of angle B.

The measure of angle B is 135°.

HW 9.2

Q19) Find the measure of angle A. Assume lines l and m are parallel.

A=30°

HW 9.3

Q1) Find the area of a rectangle 43 ft by 31 ft.

The area is

1333 ft²

HW 9.3

Q2) Find the area of a rectangle 61 ft by 54 ft.

The area is 3294 ft²

HW 9.3

Q3) Find the area.

The area is

48 in²

HW 9.3

Q4) Determine the area of the triangle.

The area is 25 cm²

HW 9.3

Q5)
Question content area top left Find the area of the circle. Use 3.14 for π.

    

The area is 50.24 m².

HW 9.3

Q6) Find the area of the circle. Use 3.14 for π.

The area is 452.16 ft²

HW 9.3

Q7) Find the area of the shaded region inside the square and between the two circles. Use π ≈3.14.

The area of the shaded region is approximately 21.5m²

HW 9.3

Q8) Find the area inside the circle and outside the square. Use π≈3.14.

A≈502.74m²

HW 9.3

Q9) Find the unknown side of the triangle.

The length of the unknown side is

13 inches.

HW 9.3

Q10) Find the length of the third side of the right triangle.

The length of the third side is approximately 8.485 cm.

HW 9.3

Q11) Find the area of the largest triangle shown on the right.

The area of the largest triangle is 174 square inches.

HW 9.3

Q12) State whether perimeter or area would be the more appropriate quantity to measure.

You are covering an archeological plot with a tarpaulin.

Area

would be the more appropriate quantity to measure.

HW 9.3

Q13) In order to purchase fencing to go around a rectangular​ yard, would you need to use perimeter or area to decide how much to​ buy?

perimeter

HW 9.3

Q14) A baseball diamond is a square with 76 Feet between each base. Determine the distance from home plate to second base.

The distance from home plate to second base is 107.480 feet.

HW 9.3

Q15) Find the length of line segment AB in the given figure.

The length of line segment AB is 2 m.

HW 9.3

Q16) Which one of the following is a better​ buy: a large pizza with a 10-inch diameter for $ 14.00 or a medium pizza with a 55​-inch diameter for $ 5.00​?

Large Pizza

HW 9.3

Q17)

A hotel owner wants to​ re-tile his lobby. Use the diagram shown to the right to determine the area to be tiled. Note that the figure to the right is not to scale.

The area to be tiled is 11,024 square feet.

HW 9.3

Q18) A design for a rectangular stone garden has a circular pond in its center, as shown. The rectangle has a length of 10 yards and a width of 12 yards. How many square yards will be covered in​ stones? Use π≈3.14.

The area covered in stone is 41.5 square yards.

HW 9.3

Q19) Fill in the blanks.

The​ _____ of a polygon is the sum of the lengths of the sides of the polygon. The​ _____ is a measure of the amount of surface that the polygon covers.

PERIMETER AND AREA