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.**

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.
**

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.

Answer:

m∠a = 56°

Explanation:

Property of a Parallelogram:

- Opposite angles are equal.

m∠a = 56°

Question 15.

Answer:

m∠b = 45°

Explanation:

Property of a Parallelogram:

- Sum of any two adjacent angles is 180°

m∠b = 180-135 =45°

Question 16.

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.

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.

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.

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:

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

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:

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.**

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.

Answer:

m∠p = 125°

Explanation:

property of a Rhombus:

- Opposite angles are equal.

m∠p= 125°

Question 30.

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.

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.

Answer:

m∠s = 52°

Explanation:

- 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.

Answer:

m∠t = 90°

Explanation:

- 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.

Answer:

m∠s = 37°

Explanation:

in triangle ABC sum of three angles is 180°

m∠s + m∠v = 180°- 106°= 74°

- 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 \(\overline{A B}\) || \(\overline{D C}\).
**

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.

Answer:

m∠A = m∠116°

m∠D = m∠64°

m∠D = 180 – 116

= 64°

Explanation:

Supplementary angles = 180°

m∠64° + m∠116° = 180°

- 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.

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.

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.

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.

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.

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.

Answer:

Explanation:

Question 47.

Answer:

Explanation:

The sum of angles in a triangle = 180

70 + 38 = 98

180 – 98 = 82