Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid

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This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 5 Parallelogram, Rhombus, and Trapezoid provides detailed solutions for the textbook questions.

Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid

Complete. Figure ABCD is a parallelogram. Measure the sides and angles of the figure.

Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 1
Explanation:

Question 1.
AD = ___ cm
Answer: AD = 6 cm
Explanation:
Property of a Parallelogram:

  • Opposite sides are equal and parallel.

Question 2.
AB _______ cm
Answer:
AB = 7 cm
Explanation:
Property of a Parallelogram:

  • Opposite sides are equal and parallel.

Question 3.
BC = __ cm
Answer:
BC = 6 cm
Explanation:
Property of a Parallelogram:

  • Opposite sides are equal and parallel.

Question 4.
DC = ______ cm
Answer:
DC = 7 cm
Explanation:
Property of a Parallelogram:

  • Opposite sides are equal and parallel.

Question 5.
m∠A = ____
Answer:
m∠A = 55°
Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.

Question 6.
m∠B = ___
Answer:
m∠B = 120°

Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.

Question 7.
m∠C = ___
Answer:
m∠C = 55°

Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.

Question 8.
m∠D = ___
Answer:
m∠D = 120°

Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.

Question 9.
Name the parallel sides of the figure. ______
Answer:
\(\overline{A B}\) || \(\overline{D C}\)
\(\overline{A D}\) || \(\overline{B C}\)

Question 10.
Name the opposite angles that are equal. ______
Answer:
m∠A = m∠C
m∠B = m∠D

This parallelogram is not drawn to scale. Fill in the blanks.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 2

Question 11.
m∠Q = m∠___
= _____
Answer:
m∠Q = m∠S = 75°

Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.

Question 12.
m∠P = 180° – ___
= ____
Answer:
m∠P = 180° – m∠S =180° – 75° = 105°

Explanation:
Property of a Parallelogram:

  • Sum of any two adjacent angles is 180°

Question 13.
m∠R = m∠___
= ____
Answer:
m∠R = m∠P =  105°

Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.

These parallelograms are not drawn to scale. Find the unknown angle measures.

Question 14.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 3
Answer:
m∠a =  56°
Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.
    m∠a =  56°

Question 15.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 4
Answer:
m∠b = 45°

Explanation:
Property of a Parallelogram:

  • Sum of any two adjacent angles is 180°
    m∠b = 180-135 =45°

Question 16.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 5
Answer:
m∠f = 46°

Explanation:
Property of a Parallelogram:

  • Sum of any two adjacent angles is 180°
    180-73=107°
    m∠f = 107 – 61 =46°

Question 17.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 6
Answer:
m∠g =  81°
Explanation:
Property of a Parallelogram:

  • Opposite angles are equal.
    So opposite angle is 139°
    m∠g =  139 -58 = 81°

Question 18.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 7
Answer:
m∠x = 90°
m∠y = 90°
m∠z = 90°

Property of a Parallelogram:

  • Opposite angles are equal.
  • Sum of any two adjacent angles is 180°
    m∠y = 90°
    m∠x = 180 -90° =90°
    m∠z = m∠x = 90°

Question 19.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 9
Answer:
m∠p = 90°

Property of a Parallelogram:

  • Sum of any two adjacent angles is 180°
    m∠p = 180-62+28= 90°

Complete. Write the name of another side or angle of each rhombus.

Question 20.
AB = BC
= ___ = ____
Answer:

Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 10
AB = BC= CD= DA
Explanation:
property of a Rhombus:

  • All sides are equal and, opposite sides are parallel to each other.
    AB = BC= CD= DA

Question 21.
m∠B = m∠______
Answer:
m∠B = m∠D
Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠B = m∠D

Question 22.
m∠A = m∠____
Answer:
m∠A = m∠C
Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠A = m∠C
    Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 11

Question 23.
UV = _______
= ___ = ___
Answer:
UV = VS= ST = TU

Explanation:
property of a Rhombus:

  • All sides are equal and, opposite sides are parallel to each other.
    UV = VS= ST = TU

Question 24.
m∠S = m∠____
Answer:

Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 11
m∠S = m∠U

Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠S = m∠U

Question 25.
m∠T = m∠______
Answer:
m∠T = m∠V

Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠T = m∠V

This rhombus is not drawn to scale. Fill in the blanks.

Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 12

Question 26.
m∠X = m∠__ = ____
Answer:
m∠X = m∠Z= 53°

Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠X = m∠Z= 53°

Question 27.
m∠W = ____ – ___ = ____
Answer:
m∠W = 180 – 53° = 127°

Explanation:
property of a Rhombus:

  • Sum of any two adjacent angles is 180°
    m∠W = 180 – m∠Z = 180 – 53° = 127°

Question 28.
m∠Y = m∠___ = ____
Answer:
m∠Y = m∠W = 127°

Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠Y = m∠W = 127°

These rhombuses are not drawn to scale. Find the unknown angle measures.

Question 29.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 13
Answer:
m∠p =  125°

Explanation:
property of a Rhombus:

  • Opposite angles are equal.
    m∠p= 125°

Question 30.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 14
Answer:
m∠q = 180 – 57° = 123°

Explanation:
property of a Rhombus:

  • Sum of any two adjacent angles is 180°
    m∠q = 180 – 57° = 123°

Question 31.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 15
Answer:

m∠r = 180 – 129° = 51°

Explanation:
property of a Rhombus:

  • Sum of any two adjacent angles is 180°
    m∠r = 180 – 129° = 51°

Question 32.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 16
Answer:
m∠s =  52°

Explanation:

property of a Rhombus:
  • All sides are equal and, opposite sides are parallel to each other.
    AB=BC=CD=DA

then in Triangle ABC AB= BC. then it is isosceles Triangle .
The isosceles triangle property states that when two sides are equal, the base angles are also equal.
So, m∠s =  52°

Question 33.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 17
Answer:
m∠t =  90°

Explanation:

property of a Rhombus:
  • All sides are equal and, opposite sides are parallel to each other.
    AB=BC=CD=DA

then in Triangle ABC AB= BC. then it is isosceles Triangle .
The isosceles triangle property states that when two sides are equal, the base angles are also equal.
So, m∠s =  45°
in triangle sum of three angles is 180°
So, m∠t = 180 -45+  45° = 90°

Question 34.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 18
Answer:
m∠s =  37°

Explanation:

in triangle ABC  sum of three angles is 180°
m∠s  + m∠v = 180°- 106°=  74°

property of a Rhombus:
  • All sides are equal and, opposite sides are parallel to each other.
    AB=BC=CD=DA

then in Triangle ABC AB= BC. then it is isosceles Triangle .
The isosceles triangle property states that when two sides are equal, the base angles are also equal.
So, m∠s =m∠v  =  74° divided by 2 = 37°

Measure the unknown angles. Then fill in the blanks. ABCD is a trapezoid where \(\overline{A B}\) || \(\overline{D C}\).
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 19

Question 35.
m∠A = ____
Answer:

Question 36.
m∠B = ___
Answer:
m∠B = 110

Question 37.
m∠C = ____
Answer:
m∠C = 70

Question 38.
m∠D = ___
Answer:
m∠D = 80

Question 39.
m∠A + m∠D = m∠___ + m∠___ = ____
Answer:
m∠A + m∠D = m∠100+ m∠80= 180
Supplementary angles = 180°

These trapezoids are not drawn to scale. Find the unknown angle measures.

Question 40.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 20
Answer:
m∠A  = m∠116°
m∠D = m∠64°
m∠D  = 180 – 116
= 64°
Explanation:
Supplementary angles = 180°
m∠64° + m∠116° = 180°

Trapezium and Its Properties
  • Angle: The sum of angles in a trapezoid-like other quadrilateral is 360°. …
  • Two angles on the same side are supplementary, that is the sum of the angles of two adjacent sides is equal to 180°.

Question 41.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 21
Answer:
m∠G = m∠58°
m∠F = m∠122°
m∠F  = 180 – 58 = 122
Explanation:
Supplementary angles = 180°
m∠58° + m∠122° = 180°

Question 42.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 22
Answer:
m∠L = m∠109°
m∠K = m∠71°
m∠K  = 180 – 109 = 71
Explanation:
Supplementary angles = 180°
m∠71° + m∠109° = 180°

Question 43.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 23
Answer:
m∠P = m∠97°
m∠Q = m∠83°
m∠Q  = 180 – 97 = 83°
Explanation:
Supplementary angles = 180°
m∠83° + m∠97° = 180°
Explanation:
m∠S = m∠81°
m∠R = m∠99°
m∠R  = 180 – 81 = 99°
Explanation:
Supplementary angles = 180°
m∠81° + m∠99° = 180°

These trapezoids are not drawn to scale. Find the unknown angle measures.

Question 44.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 24
Answer:
m∠a = 60°
Explanation:
m∠w = 30°
m∠x = 90
90 + 30 = 120
m∠a = 180 – 120 = 60°
Sum of the angles of a triangle = 180°
m∠b = 110°
m∠u = 70° given
m∠u + m∠b  = 180°
180 – 70 = 110°
110 + 70 = 180°
Supplementary angles = 180°

Question 45.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 25
Answer:
∠d = 55°
∠c = 90°
Explanation:
In quadrilateral the sum of angles = 360°
∠w = 90°
∠Y = 85°
YX = 180°
85° + 40° = 125°
180° – 125° = 55°
∠d = 55°
125° + 55° + 90° = 270°
360° – 270° = 90°
∠c = 90°

Question 46.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 26
Answer:
Explanation:

Question 47.
Math in Focus Grade 5 Chapter 13 Practice 5 Answer Key Parallelogram, Rhombus, and Trapezoid 27
Answer:
Explanation:
The sum of angles in a triangle = 180
70 + 38 = 98
180 – 98 = 82

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