Practice the problems of Math in Focus Grade 7 Workbook Answer Key Chapter 6 Review Test to score better marks in the exam.

## Math in Focus Grade 7 Course 2 B Chapter 6 Review Test Answer Key

**Concepts and Skills**

**Tell whether each pair of angles are supplementary, complementary or neither.**

Question 1.

m∠1 = 23° and m∠2 = 157°

Answer:

Explanation:

Question 2.

m∠3 = 65° and m∠4 = 25°

Answer:

Explanation:

Question 3.

m∠5 = 43° and m∠6 = 57°

Answer:

Explanation:

Question 4.

m∠7 = 82° and m∠8 = 8°

Answer:

Explanation:

Question 5.

m∠9 = 110° and m∠10 = 80°

Answer:

Explanation:

Question 6.

m∠11 = 18° and m∠12 = 62°

Answer:

Explanation:

**Tell whether the following list of angle measures are complementary or supplementary.**

m∠A = 67°, m∠B = 80°, m∠C = 131°, m∠D = 21°,

m∠E = 51°, m∠F = 46°, m∠G = 10°, m∠H = 120°,

m∠J = 69°, m∠K = 60°, m∠P = 49°, m∠Q = 113°,

m∠R = 44°, m∠S = 41°

Question 7.

Name two pairs of complementary angles.

Answer:

m∠B = 80°, m∠G = 10°

m∠F = 46°, m∠R = 44°

Explanation:

Two angles are called complementary when the measures of their angles add to 90 degrees. The two pairs of complementary angles are m∠B = 80°, m∠G = 10°. If we add both angles the sum adds up to 90°.

Question 8.

Name two pairs of supplementary angles.

Answer:

m∠A = 67°, m∠Q = 113°

m∠H = 120°, m∠K = 60°

Explanation:

Two angles are called supplementary when the measures of their angles add to 180 degrees. The two pairs of supplementary angles are m∠A = 67°, m∠Q = 113°. If we add both angles the sum adds up to 180°.

**Copy and complete.**

Question 9.

Name two pairs of angles for each type of angle pair.

Answer:

∠TBC = 60°, ∠ABR = 30° are complementary angles.

∠RBT = 120°, ∠TBC = 60°are supplementary angles.

Explanation:

The two pairs of angles for complementary angles are ∠TBC = 60°, ∠ABR = 30°.

The two pairs of angles for supplementary angles are ∠RBT = 120°, ∠TBC = 60°

**Find the measure of each numbered angle.**

Question 10.

\(\overleftrightarrow{\mathrm{AB}}\) is a straight line.

Answer:

The measurement of numbered angle 1 is 43°.

Explanation:

∠AOC + ∠BOC = 180°

1 + 137° = 180°

1 = 180° – 137°

1 = 43°

Question 11.

\(\overleftrightarrow{\mathrm{AB}}\) is a straight line.

Answer:

The measurement of numbered angle 2 is 120°.

Explanation:

∠AOD + ∠DOC + ∠COB = 180°

38° + 2 + 22° = 180°

2 + 60° = 180°

2 = 180° – 60°

2 = 120°

**Find the measure of each numbered angle.**

Question 12.

Answer:

The measurement of numbered angle 3 is 195°

Explanation:

∠AOB + ∠COB + ∠AOC = 360°

3 + 120°+ 45° = 360°

3 + 165° = 360°

3 = 360° – 165°

3 = 195°

Question 13.

\(\overleftrightarrow{\mathrm{AB}}\) is a straight line.

Answer:

The measurement of numbered angle 4 is 73°

Explanation:

∠AOD + ∠DOC + ∠COB = 180°

4 + 17° + 90° = 180°

4 + 107° = 180°

4 = 180° – 107°

4 = 73°

**Use an equation to find the value of each variable.**

Question 14.

\(\overleftrightarrow{\mathrm{AB}}\) is a straight line.

Answer:

s°= 45°, 3s°= 135°

Explanation:

∠AOC + ∠COB = 180°

3s° + s° = 180°

4s° = 180°

s° = 180 ÷ 4

s° = 45°

3s°= 135°

Question 15.

\(\overleftrightarrow{\mathrm{AB}}\) is a straight line.

Answer:

w° = 28°, 2w° =56°, 3w°=140°

Explanation:

∠AOD + ∠DOC + ∠COB = 180°

3w° + 40° + 2w° = 180°

5w° + 40° = 180°

5w° = 180° – 40°

5w° = 140°

w° = 28°

3w°= 3 × 28 = 84°

2w°= 2° × 28 = 56°

Question 16.

\(\overleftrightarrow{\mathrm{AB}}\) is a straight line.

Answer:

t° = 30°, 2t° = 30°

Explanation:

∠BOC + ∠AOD + ∠DOC = 180°

t° + 2t° + 90° = 180°

3t° + 90° = 180°

3t° = 180° – 90°

3t° = 90°

t° = 90° ÷ 3

t° = 30°

Question 17.

Answer:

v°=17°, u°=73°

Explanation:

∠AOB + ∠BOC = 90°

53° + v° = 90°

v° = 90° – 53°

v° = 17°

∠BOC + ∠COD = 90°

v° + u° = 90°

17° + u° = 90°

u° = 90° – 17°

u° = 73°

Question 18.

\(\overleftrightarrow{\mathrm{AB}}\), \(\overleftrightarrow{\mathrm{CD}}\), and \(\overleftrightarrow{\mathrm{EF}}\) are a straight line.

Answer:

r°= 22°, 4r°= 88°

Explanation:

∠COA = ∠BOD = r° (vertically opposite angles)

∠EOB + ∠BOD + ∠FOD = 180°

4r° + r° + 70° = 180°

5r° + 70° = 180°

5r° = 180° – 70°

5r° = 110°

r° = 110 ÷ 5

r° = 22°

4r° = 4 × 22 = 88°

Question 19.

Answer:

x° = 36°, 2x° = 72°, 3x° = 108°, 4x° = 144°

Explanation:

3x° + 2x° = 180°

5x° = 180°

x° = 180÷5

x° = 36°

2x° = 36 × 2 = 72°

3x° = 3 × 36 = 108°

4x° = 4 × 36 = 144°

\(\overline{M N}\) is parallel to \(\overline{P Q}\). Find the measure of each numbered angle.

Question 20.

Answer:

∠1 = 25°, ∠2 = 65°, x° = 65°

Explanation:

Let ∠QPS = x°

∠NPM + ∠NPQ + ∠QPS = 180°

90° + 25° + x° = 180°

115° + x° = 180°

x° = 180 -115°

x° = 65°

∠2 = ∠x = 65° Corresponding angles are equal

∠NMP + ∠PNM = 90°

∠2 + ∠1 = 90°

65° + ∠1 = 90°

∠1 = 90° – 65°

∠1 = 25°

Question 21.

Answer:

∠1 = 52°, ∠2 = 52°, ∠3 = 66°

Explanation:

Let ∠SOQ = x°

114°+ x° = 180°

x° = 180° – 114°

x° = 66°

x° = ∠3 = 66° (vertically opposite angles)

∠3 + ∠TSQ + ∠QSN = 180°

∠3 + 62° + ∠2 = 180°

66° + 62° + ∠2 = 180°

∠2 = 180° – 128°

∠2 = 52°

∠1 = ∠2 (vertically opposite angles)

∠1 = 52°

**Problem Solving**

**Solve. Show your work.**

**Find the value of x.**

Question 22.

Find the value of x.

Answer:

x° + 2x° = 330°

3x°= 330°

x° = 330 ÷ 3

x° = 110°

Question 23.

ABCD is a rhombus. Find the measures of ∠1 and ∠2.

Answer:

∠1 = 70°, ∠2 = 120°

Explanation:

Opposite angles in a rhombus are equal.

∠1 = 70°

∠1 + ∠2 + 70° = 360°

70° + ∠2 + 70° = 360°

∠2 + 140° = 360°

∠2 = 360° – 140°

∠2 = 120°

Question 24.

ABCD is a rectangle. \(\overline{\mathrm{AE}}\) and \(\overline{\mathrm{DC}}\) are straight lines. ∠FBG is a right angle, m

ABF = 74°, and m∠BEG = 42°. Find the measures of ∠EBG and ∠BGC.

Answer:

x=∠EBG =16°, ∠BGC = 122°

Explanation:

74° + 90° + x° = 180°

x° = 180° – 164°

x° = 16°

16° + 42° + ∠BGC = 180°

∠BGC = 180° – 58°

∠BGC = 122°

Question 25.

The diagram shows the flag of the United Kingdom. m∠MNR = 90°. Name two pairs of complementary and supplementary angles.

Answer:

∠MNQ, ∠SNP, ∠QNS are complementary angles.

∠MNR, ∠MNQ, ∠SNP are supplementary angles.

Explanation:

The two pairs of angles for complementary angles are ∠MNQ, ∠SNP, ∠QNS.

The two pairs of angles for supplementary angles are ∠MNR, ∠MNQ, ∠SNP.

Question 26.

m∠1 = 15° and m∠2 = 131°. \(\overleftrightarrow{\mathrm{AB}}\) is a straight line. Find the measure of ∠3.

Answer:

∠3 = 34°

Explanation:

m∠1 + m∠2 + m∠3 = 180°

15° + 131° + m∠3 = 180°

m∠3 + 146° = 180°

m∠3 = 180° – 146°

m∠3 = 34°

Question 27.

The diagram shows ∠1 and ∠2, which are formed by \(\overleftrightarrow{M N}\) intersecting \(\overleftrightarrow{P Q}\) and \(\overleftrightarrow{R S}\). In the diagram, m∠1 = (12x + 7)°, m∠2 = (10x + 15)°, and x = 4. Explain how you know that \(\overleftrightarrow{P Q}\) is parallel to \(\overleftrightarrow{R S}\).

Answer:

Parllel lines are lines that are always the same distance apart and will never intersect. Hence in the given figure the lines \(\overleftrightarrow{P Q}\) is parallel to \(\overleftrightarrow{R S}\).

And iif two lines are parllel the corresponding angles are equal. Therefore ∠1 = ∠2

Explanation:

m∠1 = m∠2 are corresponding angles

(12x + 7)° = (10x + 15)°

12x – 10x = 15 – 7

2x = 8

x° = 8 ÷ 2

x° = 4°

(12x + 7)° = 12 × 4 + 7 = 48 + 7 = 55°

(10x +15)° = 10 × 4 + 15 = 40 + 15 = 55°

Question 28.

In the diagram, m∠1 = (5x – 20)°, m∠2 = (2x + 14)°, and m∠3 = 18°. Use an equation to find the measures of ∠1 and ∠2.

Answer:

∠1 = 100°, ∠2 = 62°, ∠3 = 24°

Explanation:

m∠1 + m∠2 + m∠3 = 180°

(5x – 20)° + (2x + 14)° + 18° =180°

7x – 6 + 18° = 180°

7x +12 = 180°

7x = 180° – 12°

7x = 168°

x°= 24°

5x – 20 = 5 × 24 – 20 = 120 – 20 =100°

2x + 14 = 2 × 24 + 14 = 62°

∠1 = 100°, ∠2 = 62°, ∠3 = 24°