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°
