This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Practice 1 Angles on a Line provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 12 Practice 1 Answer Key Angles on a Line

**In each figure, \(\overleftrightarrow{A C}\) is a line. Use a protractor to find the unknown angle measures.**

Question 1.

m∠DBC = ____

m∠DBA = ____

m∠DBC + m∠DBA = ___ + _____

= _____

Answer:

m∠DBC = 60°

m∠DBA = 120°

m∠DBC + m∠DBA = 60° + 120°= 180°

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Then take a protractor and measure m∠DBC = 60°

Then subtract m∠DBC = 60° from 180°,

We get m∠DBA = 120°

Question 2.

m∠x = ____

m∠y = ____

m∠x + m∠y = ___ + ___

= _____

Answer:

m∠x = 70°

m∠y = 110°

m∠x + m∠y = 70° + 110° = 180°

Explanation:

To measure the unknown angles, first take a protractor and measure m∠x = 70°

Then measure m∠y = 110°

Add both the angles m∠x + m∠y = 70° + 110° = 180°

**\(\overleftrightarrow{A C}\) is a line. Use a protractor to find the unknown angle measures.**

Question 3.

m∠p = ____

m∠q = ____

m∠r = ____

m∠p + m∠q + m∠r = ___ + ___ + ___

= ____

Answer:

m∠p = 20°

m∠q = 100°

m∠r = 60°

m∠p + m∠q + m∠r = 20° + 100° + 60°= 180°

Explanation:

To measure the unknown angles, first take a protractor and measure m∠p = 20°

Then measure m∠q = 100°

Then measure m∠r = 60°

Add all the angles m∠p + m∠q + m∠r = 20° + 100° + 60° = 180°

**Name the angles on each line.**

Question 4.

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

Answer:

m∠XYW = 40°

m∠WYZ = 140°

m∠XYW + m∠WYZ = 40°+ 140° = 180°

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Then take a protractor and measure m∠XYW = 40°, an angle less than 90° is acute angle.

Then take a protractor and measure m∠WYZ = 140°, an angle more than 90° is obtuse angle.

Add both the angles m∠XYW + m∠WYZ = 40°+ 140° = 180°

Question 5.

\(\overleftrightarrow{P R}\) is a line.

Answer:

m∠PQS = m∠a = 40° Acute Angle

m∠TQS = m∠b = 90° Right Angle

m∠TQR = m∠c = 50° Acute Angle

m∠PQS + m∠TQS + m∠TQR = 40°+ 90° + 50° = 180° Straight Angle

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Then take a protractor and measure m∠PQS = m∠a = 40° Acute Angle, an angle less than 90° is acute angle.

Then take a protractor and measure m∠TQS = m∠b = 90° Right Angle.

Then take a protractor and measure m∠TQR = m∠c = 50° Acute Angle

Add all the angles m∠PQS + m∠TQS + m∠TQR = 40°+ 90° + 50° = 180° Straight Angle.

**Name each set of angles on a line.**

Question 6.

\(\overleftrightarrow{A C}\) is a line.

Answer:

m∠p = 50°

m∠q = 120°

m∠r = 60°

m∠s = 60°

m∠t = 70°

∠p + ∠q + ∠r + ∠s + ∠t = 50° + 120° + 60°+ 60°+ 70° = 360°

Explanation:

m∠p and m∠q are Vertical angles where the two angles cross each other.

m∠r , m∠t and m∠s are acute angle, where the angle is less than 90°

Question 7.

\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\) are line.

Answer:

∠p = 60°

∠q = 100°

∠r = 20°

∠s = 160°

∠t = 20°

∠p + ∠q + ∠r + ∠s + ∠t = 60° + 100° + 20°+ 160°+ 20° = 360°

Explanation:

∠p, ∠r and ∠t are acute angles, where the angle is less than 90°

∠q and ∠s are obtuse angles, where the angles is more than 90°

**Find the unknown angle measures.**

Question 8.

\(\overleftrightarrow{A C}\) is a line. Find the measure of ∠DBC.

Answer:

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Given m∠DBC + 125° = 180°

m∠DBC – 180° = 125° = 55°

Question 9.

\(\overleftrightarrow{E G}\) is a line. Find the measure of ∠HFE.

Answer:

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Given ∠FIG = 42° = 180°

∠HFI = 90°

∠EFH = 180° – (42° + 90°)

= 180° – 132° = 48°

**Find the unknown angle measures.**

Question 10.

\(\overleftrightarrow{O Q}\) is a line. Find the measure of ∠SPT.

Answer:

m∠SPT =180° – (15°+70°+39°) = 56°

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Given ∠POR = 15°

∠RPS = 70°

∠TPQ = 39°

m∠SPT = 180° – (∠POR +∠RPS +∠TPQ )

m∠SPT =180°- (15°+70°+39°) = 56°

Question 11.

\(\overleftrightarrow{A C}\) is a line. Find the measure of ∠EBF.

Answer:

m∠EBF =180° – (41° + 27° + 90°) = 180° – 158° = 22°

Explanation:

To determine to measure of the unknown angle, be sure to use the total sum of 180°.

Given ∠DBA = 41°

∠DBE = 27°

∠FBC = 90°

m∠EBF = 180° – (∠DBA +∠DBE +∠FBC )

m∠EBF =180°- (41°+27°+90°) = 22°

Question 12.

\(\overleftrightarrow{J K}\) is a line. Find the measure of ∠y and ∠z.

Answer:

Explanation:

Angles formed by two rays lie in the plane that contains the rays.

Angles are also formed by the intersection of two planes.

Given:

∠JOI = 80°

∠JOG = 36°

∠GOH= 72°

m∠y = 180° – (∠JOG+∠GOH)

m∠y =180°- (36°+72°)

=180°- 108°

= 72°

m∠z =180°- ∠JOI

= 180° – 80°

= 100°

Question 13.

\(\overleftrightarrow{E F}\) and \(\overleftrightarrow{G H}\) are line. Find the measure of ∠a and ∠b.

Answer:

Explanation:

Angles formed by two rays lie in the plane that contains the rays are called vertex of the angle.

Angles are also formed by the intersection of two planes.

Given:

∠GOF = 160°

∠FOH = 20°

∠HOJ= 50°

∠JOI = 90°

m∠a =180°- ∠GOF

= 180° – 160°

= 20°

m∠b= 180° – (∠HOJ+∠FOH+∠JOI )

=180°- (50°+20°+90°)

=180°- 160°

= 20°