We included HMH Into Math Grade 4 Answer Key PDF Module 13 Lesson 6 Join and Separate Angles to make students experts in learning maths.
HMH Into Math Grade 4 Module 13 Lesson 6 Answer Key Join and Separate Angles
I Can find the measure of angles that are joined or separated.
Step It Out
Question 1.
In following directions to build a model bridge, Rosie cuts a 90° angle into two parts. Then she joins the parts to make the whole angle. What can you say about the sum of the measures of the two angles as compared with the measure of the whole angle?
A. Use a protractor to draw a 90° angle on a piece of paper. Label it ∠ABC.
Answer:
Explanation:
Draw a line segment AC.
Taking A as center and using a compass draw an arc of some radius, that cuts at B.
Taking C as center and with same radius draw an arc, that cuts the first arc at B.
Then draw a ray from B to center of AC.
B. Cut out ∠ABC. Draw point G somewhere inside ∠ABC.
Answer:
Explanation:
∠ABC is a whole, by drawing BG we point G with an angle of 90 degrees.
C. Draw \(\overrightarrow{B G}\) and cut along the ray to make two separate angles.
Answer:
Explanation:
By drawing a ray BG to separate angles along the whole as ∠BAG and ∠BGC
D. Use a protractor to measure the angles and record the measures.
? _________ = _________
? _________ = _________
Answer:
∠BAG = ∠BCG = 90°
∠GAB = ∠GCB = 90°
Explanation:
Protractor is used to measure the angles.
E. Now join the angles. Write an equation to model the angles.
Answer:
90° + 90° = 180° COMPLETE ANGLE
Explanation:
∠ABG = 90°
∠BCG = 90°
The sum of the two parts is whole.
90° + 90° = 180°
F. Rosie can find the measure of each new angle by ____________.
Answer:
By using a protractor.
Explanation:
Protractor is used to measure the angles.
Turn and Talk If Rosie cuts the 90° angle into 3 parts, what can you conclude about the sum of the measures of the 3 angles? Explain.
Answer:
Sum of 3 angles 90°
Explanation:
If Rosie wants to cut the 90° angle into 3 equal parts,
she get the sum of the measures of the 3 angles as 30°
Question 2.
Use the measure of each angle in the circle to write an equation that shows how the angles join together.
A. Use a protractor to find the measure of each angle.
Answer:
Explanation:
Line up the vertex of the angle with the dot at the center of the protractor.
Line up one side of the angle with 0 degrees on the protractor,
than see where the other side of the angle crosses the number scale.
B. Label each angle with its measure.
Answer:
∠PMO = 90°
∠NMO =70°
∠NML = 50°
∠PML = 150°
Explanation:
By using the protractor one can measure the angles as explained above.
C. Write an equation to find the whole.
Answer:
∠PMO + ∠NMO + ∠NML + ∠PML = 360°
90° + 70° + 50°+ 150° = 360°
Explanation:
A complete whole is 360° which is divided into 4 unequal parts as shown above.
Angles of each parts are 90°, 70°, 50°, 150°
Sum of the 4 angles is 90° + 70° + 50°+ 150° = 360°
Question 3.
The sum of the two angle measures is 135°. One angle measures 45°. What is the measure of the other angle?
A. Write an equation to find the part.
Answer:
135° – 45° = 90°
Explanation:
Given the sum of the two angles is 35°
one of the angle is 45°
unknown angle be x
135° – 45° = x
x = 90°
B. The measure of the other angle is ________.
Answer:
90°
Explanation:
By subtracting the part of angle from the whole angle,
we get the other angle.
135° – 45° = 90°
Check Understanding
Question 1.
Add to find the measure of ∠ABC. Write an equation to record your work.
m?ABC = _________
Answer:
m∠ABC = 80°
Explanation:
m∠ABC = m∠ABD + m∠DBC
m∠ABC = 46° + 34° = 80°
Question 2.
Given \(\overleftrightarrow{Q S}\), what is the measure of ∠QRT?
m?QRT =?__________
Answer:
m∠QRT = 95°
Explanation:
m∠QRS = 180°
m∠TRS = 85°
m∠QRT = m∠QRS – m∠TRS
= 180° – 85° = 95°
On Your Own
Question 3.
Reason ∠QRS is a straight angle. Without measuring, could the measures of ∠QRP and ∠PRS be 70° and 115°? Explain.
Answer:
∠QRS = 180°
Explanation:
∠QRS = ∠PRS + ∠QRP = 115° + 70° = 180°
∠QRP = ∠QRS – ∠PRS = 180° – 115° = 65°
∠PRS = ∠QRS – ∠QRP = 180° – 70° = 110°
Question 4.
Reason ∠BCD is a straight angle. Without measuring, could the measures of ∠BCE and ∠ECD be 162° and 18°? Explain.
Answer:
Yes, ∠BCD = 180°
Explanation:
∠BCD is a straight angle = 180°
∠BCD = 180°
∠BCE = ∠BCD – ∠ECD = 180° – 18° = 162°
Use Tools Use a protractor to find the measure of each angle. Label each angle with its measure. Write the sum of the angle measures as an equation.
Question 5.
Answer:
∠AOB + ∠BOC = 70° + 80° = 150°
Explanation:
∠AOB = 70°
∠BOC = 80°
Sum of the angles are ∠AOB + ∠BOC = 70° + 80° = 150°
Question 6.
Answer:
∠POQ + ∠QOR = 30° + 55° = 85°
Explanation:
Given angles are ∠POQ = 30° and ∠QOR = 55°
Sum of the angles are ∠POQ + ∠QOR = 30° + 55° = 85°
Question 7.
Add to find the measure of the angle. Write an equation to record your work.
m∠URS = __________
Answer:
m∠URS = m∠URT + m∠TRS
m∠URS = 70° +85° = 155°
Explanation:
Given angles and their measures are as follows,
m∠URT = 70° and m∠TRS = 85°
m∠URS = m∠URT + m∠TRS
m∠URS = 70° +85° = 155°
Question 8.
The sum of the two angle measures is 155°. Subtract to find the measure of ∠DAC. Write an equation to record your work.
m∠DAC = _________
Answer:
m∠DAC = m∠DAB – m∠CAB
m∠DAC = 155° – 110° = 45°
Explanation:
Given angles and their measures are as follows,
m∠DAC = 155° and m∠CAB = 110°
m∠DAC = m∠DAB – m∠CAB
m∠DAC = 155° – 110° = 45°
Question 9.
Open Ended Draw to show two different ways to separate an angle with a measure of 120° into 3 parts.
How does the measure of an angle compare to the sum of its parts?
Answer:
30° + 30° + 60° = 120°
40° + 40° + 40° = 120°
Explanation:
Sum of the angles in triangle is 120°
Complete angle 120° is shown in 2 two different sums.
30° + 30° + 60° = 120°
40° + 40° + 40° = 120°
Use a protractor to find the measure of each angle. Label each angle with its measure. Write the sum of the angle measures as an equation.
Question 10.
Answer:
Sum of the angles is 360 degrees.
Explanation:
m∠HGJ = 180°
m∠HGI = 140°
m∠IGJ = 40°
Sum of the 3 angles are m∠HGJ + m∠HGI + m∠IGJ
180° + 140° + 40° = 360°
Question 11.
Answer:
Sum of the 3 angles are 360°
Explanation:
m∠QRT = 180°
m∠QRU = 90°
m∠URT = 90°
m∠SRT = 65°
m∠SRQ = 115°
Sum of the angles are 180° + 65° + 115° = 360°