This handy Math in Focus Grade 5 Workbook Answer Key Chapter 12 Practice 3 Vertical Angles provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 12 Practice 3 Answer Key Vertical Angles

**Complete.**

Question 1.

\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\) meet at O. Use a protractor to find unknown angle measure

m∠w = _______

m∠x = __________

m∠y = _____

m∠z = __________

m∠____ = m∠______

∠___________ and ∠___________ are vertical angles.

m∠____ = m∠______

∠___________ and ∠___________ are vertical angles.

Answer:

m∠w = 50°

m∠x = 130° = 180 ° – 50°

m∠y = 50°

m∠z = 130°

m∠w = m∠y

Vertical angles are a pair of opposite angles formed by intersecting lines

∠w and ∠y are vertical angles.

m∠x = m∠z

∠x and ∠z are vertical angles.

Explanation:

As can be seen from the figure above, when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

Question 2.

\(\overleftrightarrow{X Z}\) and \(\overleftrightarrow{V W}\) meet at Y. Use a protractor to find unknown angle measures.

m∠XYW = _______

m∠WYU = __________

m∠UYZ = _____

m∠ZYV = __________

m∠VYX = ______

∠___________ and ∠___________ are vertical ongles.

∠___________ and ∠___________ are vertical angles.

Answer:

m∠XYW = 40°

m∠WYU = 90°

m∠UYZ = 50°

m∠ZYV = 40°

m∠VYX = 140°

∠XYW and ∠VYZ are vertical ongles.

∠WYZ and ∠XYV are vertical angles.

Explanation:

As can be seen from the figure above, when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

**Complete.**

Question 3.

Look at the star and its marked angles. In the table below, write three sets of:

a. angles on a line,

b. angles at a point,

c. vertical angles.

Answer:

Draw.

Explanation:

The common point where two rays meet is called the vertex and the rays are called arms of the angle or Angle on lines.

Angles on line add upto 180°

An angle is measured with reference to a circle with its center at the common endpoint of the rays.

Hence, the sum of angles at a *point* is always 360°

When two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

Question 4.

Draw rays at P to form

a. an angle whose measure forms a sum of 180° with the measure of ∠x,

Answer:

x= 30°

30° x 6 = 180°

Explanation:

The common point where two rays meet is called the vertex and the rays are called arms of the angle or Angle on lines.

Angles on line add upto 180°

b. an angle whose measure is equal to the measure of ∠x.

(Do not use a protractor to draw the angles.)

a.

b.

Answer: 30°

Explanation:

An angle measures less than 90 degrees is called acute angle.

**Find the unknown angle measures.**

Question 5.

\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\) meet at O. Find the measure of ∠COB.

Answer:

m∠COB = 130°

Explanation:

180 – 130 = 50°

Vertical angles are a pair of opposite angles formed by intersecting lines.

∠AOD and ∠COB are vertical angles.

m∠AOD = m∠COB = 130°

Question 6.

\(\overleftrightarrow{E F}\) and \(\overleftrightarrow{G H}\) meet at O. Find the measures of ∠GOF and ∠EOH.

Answer:

m∠GOF = 132° and

m∠EOH = 132°

Explanation:

180° – 48° = 132°

Vertical angles are a pair of opposite angles formed by intersecting lines

∠GOF and ∠EOH are vertical angles.

m∠GOF = m∠EOH = 132°

Question 7.

\(\overleftrightarrow{R S}\) and \(\overleftrightarrow{P Q}\) meet at N. Find the measures of ∠PNR, ∠RNQ, and ∠QNS.

Answer:

m∠PNR = 20°

m∠RNQ = 160°

m∠QNS = 20°

Explanation:

∠PNR = 180° – 160° = 20°

Vertical angles are a pair of opposite angles formed by intersecting lines

**Find the unknown angle measures.**

Question 8.

\(\overleftrightarrow{J K}\) and \(\overleftrightarrow{L M}\) meet at O. Find the measure of ∠NOK.

Answer:

∠NOK = 56°

Explanation:

∠LOJ = 180° – 108° = 72°

∠NOK = 180° -(52° + 72°)

=180° – 124°

=56°

Question 9.

\(\overleftrightarrow{A B}\), \(\overleftrightarrow{C D}\) and \(\overleftrightarrow{E F}\) meet at O. Find the measure of ∠x.

Answer:

m∠x = 120°

Explanation:

As can be seen from the figure below, when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

∠AOF and ∠EOB are vertical angles

Question 10.

\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\) meet at O. Find the measure of ∠w.

Answer:

m∠w = 75°

Explanation:

As can be seen from the figure above, when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

**Find the unknown angle measures.**

Question 11.

\(\overleftrightarrow{Q R}\) and \(\overleftrightarrow{S T}\)meet at O. Find the measures of ∠QOS, ∠TOR, and ∠SOR.

Answer:

m∠QOS = 20°

m∠TOR= 20°

m∠SOR = 160°

Explanation:

As can be seen from the figure below, when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

Question 12.

\(\overleftrightarrow{A B}\) and \(\overleftrightarrow{C D}\)meet at O. Find the measures of ∠p, ∠q, and ∠r.

m∠p = ____

m∠q = ____

m∠r = ____

Answer:

m∠p = 25°

m∠q = 155°

m∠r = 65°

Explanation:

As can be seen from the figure below, when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

Question 13.

\(\overleftrightarrow{U V}\), \(\overleftrightarrow{W X}\), and \(\overleftrightarrow{Y Z}\) meet at O. Find the measure of ∠UOW.

Answer:

Explanation:

when two lines intersect, four angles are formed.

Each opposite pair are called vertical angles and are always congruent.

68° + 72° = 140

∠UOW = 180° -140° = 40°

Question 14.

\(\overleftrightarrow{A B}\), \(\overleftrightarrow{C D}\), and \(\overleftrightarrow{E F}\) meet at O. Find the measures of ∠x and ∠y.

Answer:

m∠x = 30°

m∠y = 60°

Explanation:

∠AOB = 180° – (∠AOC + ∠FOB)

= 180° – (90° + 60°)

= 180° – 150° = 30°