This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Practice 2 Angles at a Point provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 12 Practice 2 Answer Key Angles at a Point

**In each figure, the rays meet at a point. Use a protractor to find unknown angle measures.**

Question 1.

m∠a = ___

m∠b = ___

m∠c = ____

m∠a + m∠b + m∠c = ___ + ___ + ___

= ____

Answer:

m∠a = 120°

m∠b = 90°

m∠c = 150°

m∠a + m∠b + m∠c = 120° + 90° + 150° = 360°

Explanation:

Angle less than 180° is obtuse angle.

m∠a = 120°

m∠c = 150°

Angle 90° is Right angle triangle.

m∠b = 90°

Add all the angles to get a complete angle.

m∠a + m∠b + m∠c = 120° + 90° + 150° = 360°

Question 2.

m∠AOB = ___

m∠BOC = ___

m∠COD = ____

m∠DOE = _____

m∠AOE = ____

m∠AOB + m∠BOC + m∠COD + m∠DOE + m∠AOE

= ___ + ___ + ___ + ___ + ____

= ____

Answer:

m∠AOB = 140°

m∠BOC = 40°

m∠COD = 50°

m∠DOE = 100°

m∠AOE = 30°

m∠AOB + m∠BOC + m∠COD + m∠DOE + m∠AOE

= 140°+40°+50°+100°+30°= 360° is called a complete angle.

Explanation:

m∠AOB = 140°

m∠DOE = 100°

Angle less than 180° is obtuse angle.

m∠BOC = 40°

m∠COD = 50°

m∠AOE = 30°

Angle 90° is Right angle triangle.

Add all the angles to show complete angle.

m∠AOB + m∠BOC + m∠COD + m∠DOE + m∠AOE

= 140°+40°+50°+100°+30°= 360°

**Name the angles at a point.**

Question 3.

Answer:

∠a = 120°

∠b= 80°

∠c = 160°

∠a + ∠b + ∠c = 120° + 80° + 160° = 360°

Explanation:

∠a = 120° and ∠c = 160° are obtuse angles.

∠b = 80° is acute angle.

∠a + ∠b + ∠c = 120° + 80° + 160° = 360°

Question 4.

Answer:

m∠XOW = 40°

m∠ZOW = 90°

m∠ZOY = 140°

m∠XOY=90°

m∠XOY + m∠XOW + m∠ZOW + m∠ZOY + m∠XOY

= 40° + 90° + 140° + 90° = 360°

Explanation:

In the above picture

m∠ZOW = 90° and m∠XOY=90° are right angles.

m∠XOW = 40° is acute angle as the angle is less than 90°

m∠ZOY = 140° is obtuse angle as the angle is less than 180°

Add all the angles to get complete angle.

m∠XOY + m∠XOW + m∠ZOW + m∠ZOY + m∠XOY

= 40° + 90° + 140° + 90° = 360°

Question 5.

Answer:

∠a = 60°

∠b= 120°

∠c = 60°

∠d= 120°

∠a + ∠b + ∠c +∠d = 60°+ 120° + 60° + 120° = 360°

Explanation:

As shown in the above picture

∠a + ∠c= 60° are acute angles as the angle is less than 90°

∠b and ∠d = 120° are obtuse angles as the angle is less than 180°

Add all the angles to get complete angle.

∠a + ∠b + ∠c +∠d = 60°+ 120° + 60° + 120° = 360°

Question 6.

Answer:

∠e = 90°

∠f = 90°

∠g = 30°

∠h = 100°

∠k = 50°

∠e + ∠f + ∠g +∠h + ∠k = 90° + 90°+ 30° + 100° + 50° = 360°

Explanation:

As shown in the above picture

∠g = 30° and ∠k= 50° are acute angles as the angle is less than 90°

∠e = 90° and ∠f= 90° are right angles as the angle is 90°

∠h = 100° is obtuse angle as the angle is less than 180°

Add all the angles to get complete angle.

∠e + ∠f + ∠g +∠h + ∠k = 90° + 90°+ 30° + 100° + 50° = 360°

**Find the unknown angle measures.**

Question 7.

Find the measure of ∠AOB.

Answer: 114°

Explanation:

complete angle is 360°

∠AOC +∠COB = 104° + 142° = 246°

∠AOB = 360° – 246° = 114°

Question 8.

Find the measure of ∠a.

Answer: 270°

Explanation:

complete angle is 360°

360°- 90° = 270°

Question 9.

Find the measure of ∠b.

Answer: 50°

Explanation:

complete angle is 360°

360°- 310° = 50°

Question 10.

Find the measure of ∠c.

Answer: 294°

Explanation:

complete angle is 360°

given information

40°+ 26° = 66°

360°- 66° = 294°

**Find the unknown angle measures.**

Question 11.

Find the measure of ∠q.

Answer: 150°

Explanation:

complete angle is 360°

given information

90°+37°+ 83° = 210°

360°- 210° = 150°

Question 12.

Find the measure of ∠r.

Answer: 68°

Explanation:

complete angle is 360°

given information

90°+90°+ 112° = 292°

360°- 292° = 68°

Question 13.

Find the measure of ∠a.

Answer: 106°

Explanation:

complete angle is 360°

given information

90°+164° = 254°

360°- 292° = 106°

Question 14.

\(\overleftrightarrow{P R}\) and \(\overleftrightarrow{T U}\) meet at Q. Find the measures of ∠PQSand ∠TQR.

Answer:

m∠PQS = 54°

m∠TQR = 105°

Explanation:

complete angle is 360°

given information

∠PQT = 75° = ∠UQR

∠PQS = 180° – 51° + 75° = 54°

∠TQR = 180° – 75° = 105°