This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Angles provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 12 Answer Key Angles

**Math Journal**

**Check the box for each correct statement. Then explain your answer.**

Question 1.

\(\overleftrightarrow{X Y}\) is a line.

Answer:

Explanation:

The XY is a line and the angle on a straight line is 180°, known as straight angle.

Angle POQ is 90° as per the given information in the diagram.

180° – 90° = 90°

Angle ∠XOP and ∠YOQ are equal angle = 45°

Question 2.

\(\over left right arrow{A B}\) and \(\over left right arrow{C D}\) meet at O.

Answer:

Explanation:

\(\over left right arrow{A B}\) is a line and \(\over left right arrow{C D}\) is a line are crossed at O, the opposite angles are same.

So, m∠e = m∠h and

m∠f + m∠g = m∠j are true statements.

**Put On Your Thinking Cap!**

**Challenging Practice**

**Find the unknown angle measures. Explain.**

Question 1.

\(\over left right arrow{G J}\) is a line. ∠LHK is a right angle. Find the measure of ∠LHJ.

Answer: 65°

Explanation:

Given information

GJ is a straight line, ∠LHK = 90°

∠JHK = 180° – ∠JHK

= 180° – 155° = 25°

∠JHK = ∠LHK – ∠JHK

= 90° – 25° = 65°

Question 2.

\(\over left right arrow{M N}\) and \(\over left right arrow{X Y}\) meet at O and m ∠a = m ∠b. Find the measure of ∠c.

Answer: 135°

Explanation:

\(\over left right arrow{X Y}\) is a line and \(\over left right arrow{M N}\) is a line are crossed at O, the opposite angles are same.

given information m∠a = m∠b and ∠XOP = 90

as XOY is a straight line, the angle is 180°

90° + m∠a + m∠b = 180°

∠c = 180° -∠XOM= 180 – 45° = 135°

Question 3.

\(\over left right arrow{A C}\) is a line. ∠ABE and ∠DBF are right angles. Find the measure of ∠FBC.

Answer: 26°

Explanation:

∠ABE and ∠DBF = 90°

∠EBF = ∠DBF – ∠DBE

= 90° – 26° = 64°

∠ABD = ∠ABE – ∠DBE

= 90° – 26° = 64°

∠FBC = 180 – (∠ABE + ∠EBF)

= 180° – (90° + 64°)

=180° – 154° = 26°

Question 4.

\(\over left right arrow{A B}\) and \(\over left right arrow{W X}\) meet at O. ∠YOX are right angles. Find the measures of ∠AOX and ∠COY.

Answer:

∠AOX = 124°

∠COY = 56°

Explanation:

90° – 56° = 34°

90° – 34° = 56°

∠COY = ∠COB – ∠BOY

= 90° – 34° = 56°

∠AOX = ∠WOX – ∠AOW

=180°- 56° = 124°

**Put on Your Thinking cap!**

**Problem Solving**

**Solve.**

Question 1.

\(\over left right arrow{J K}\) and \(\over left right arrow{L M}\) are lines.

Check the box for each correct statement.

Answer:

\(\over left right arrow{J K}\) and \(\over left right arrow{L M}\) are lines.

Explanation:

\(\over left right arrow{J K}\) is a line and \(\over left right arrow{L M}\) is a line are crossed at O, the opposite angles are same.

so, m∠r + m∠s = m∠p + m∠q is the wrong statement.

Question 2.

\(\over left right arrow{A B}\), \(\over left right arrow{C D}\), and \(\over left right arrow{E F}\) meet at O. Find the sum of the measures of ∠AOC, ∠FOD, and ∠BOE.

m∠AOC + m∠FOD + m∠BOE = _____

Answer: 180°

Explanation:

m∠AOC = 45°

m∠FOD = 45°

m∠BOE = 90°

m∠AOC + m∠FOD + m∠BOE = 180°

Question 3.

ABCD is a square. \(\over right arrow{B E}\) is a ray. Find the measure of ∠x.

Answer: 135°

Explanation:

As BE is a straight line and the angle is 180° at point D

and a square is ABCD is with 90° angle formed at point D

the ange ∠EDC is 135° angle ∠CDB is 45° and ∠ADB is also 45°

now the

∠x = ∠EDB – ∠ADB

= 180° – 45° = 135°

Question 4.

How many degrees does the hour hand of a clock turn between 3 P.M. and 7:30 P.M.?

Answer: 135°

Explanation:

Hour hand at 3PM is at 3 and 7:30 as shown in the clock diagram

Total angle is 360°, keep it in mind

and 360° divide in 12 parts

each part is of 30°

from hours hand 3 to 7 :30 its 135°

Question 5.

\(\over left right arrow{A B}\) is a line. The measures of ∠a and ∠b are whole numbers.

If the measure of ∠b is twice that of ∠a, find the measures of ∠a and ∠b.

Answer:

**∠a = 60°
∠b = 120°
**

Explanation:

Here the hint is angle ∠b is twice that of ∠a, and The AB is a line and the angle on a straight line is 180, known as straight angle

∠b + ∠a = 180°

2∠a + ∠a = 180°

3∠a = 180°

∠a = 180°/3 = 60°

∠a = 60°

**∠a = 60°**

∠b = 2x∠a = 120°

∠b = 2x∠a = 120°