# Texas Go Math Grade 4 Lesson 14.4 Answer Key Join and Separate Angles

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## Texas Go Math Grade 4 Lesson 14.4 Answer Key Join and Separate Angles

Essential Question

How can you determine the measure of an angle separated into parts?

Investigate

Materials

• construction paper
• scissors
• protractor

A. Use construction paper. Draw an angle that measures exactly 70Â°. Label it âˆ ABC.
The measure of angle 70Â° is

B. Cut out âˆ ABC.

C. Form two new angles from âˆ ABCby cutting it into two parts. Begin cutting at the vertex and cut between the rays.
What figures did you form? ____________

D. Use a protractor to measure the two angles you formed.
Record the measures. ____________

E. Find the sum of the angles you formed.

Math Idea: You can think of âˆ ABC as the whole and the two angles you formed as the parts of the whole.

F. Join the two angles. Compare the mâˆ ABC to the sum of the measures of its parts. Explain how they compare.

Make Connections

Materials
protractor

You can write the measure of the angles shown in a circle as a sum.

STEP 1 Use a protractor to find the measure of each angle.
STEP 2 Label each angle with its measure.
STEP 3 Write the sum of the angle measures as an equation.

Math Talk

Mathematical Processes
Describe the angles shown in the circle above using the words whole and part.

Share and Show

Add to find the measure of the angle. Write an equation to record your work.

Question 1.

mâˆ PQT = ____________
mâˆ PQT = 80Â°.

Explanation:
The equation of mâˆ PQT is
mâˆ PQT = 43Â°+37Â°
= 80Â°.

Go Math Answer Key Grade 4 Join and Separate Angles Question 2.

mâˆ JKL = ______________
mâˆ JKL = 100Â°.

Explanation:
The equation of mâˆ JKL is
mâˆ JKL = 90Â°+10Â°
= 100Â°.

Question 3.

mâˆ RHS = ______________
mâˆ RHS = 160Â°,

Explanation:
The equation of mâˆ RHS is
mâˆ RHS = 55Â°+27Â°+78Â°
= 160Â°.

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 4.

mâˆ KLM = 160Â°,
mâˆ KLJ = 80Â°,
mâˆ LMJ = 120Â°.

Explanation:
By measuring each angle is
mâˆ KLM = 160Â°,
mâˆ KLJ = 80Â°,
mâˆ LMJ = 120Â°,
and the sum of the angle measures as an equation is 160Â°+80Â°+120Â° = 360Â°.

Question 5.

mâˆ WVZ = 90Â°,
mâˆ YVZ = 90Â°,
mâˆ WVX = 140Â°,
mâˆ YVX = 40Â°.

Explanation:
By measuring each angle
mâˆ WVZ = 90Â°,
mâˆ YVZ = 90Â°,
mâˆ WVX = 140Â°,
mâˆ YVX = 40Â°,
and the sum of the angle measures as an equation is 90Â°+90Â°+140Â°+40Â° = 360Â°.

Unlock the Problem

H.O.T. Multi-Step Stephanie, Kay, and Shane each ate an equal-sized piece of a pizza. The measure of the angle of each piece was 45Â°. When the pieces were together, what is the measure of the angle they formed?
(A) 90Â°
(B) 135Â°
(C) 180Â°
(D) 225Â°
B.

Explanation:
Given that Stephanie, Kay, and Shane each ate an equal-sized piece of a pizza and the measure of the angle of each piece was 45Â°. So the measurement of the angle formed is 45Â°+45Â°+45Â° which is 135Â°.

a. What are you asked to find?
Here, asked to find the measurement of the angle formed.

b. What information do you need to use?
Here, we need information about the angle of each piece of pizza.

c. Justify Tell how you can use addition to solve the problem.
Here, we have used addition to know the measurement of the pizza.

d. Fill in the bubble for the correct answer choice above.

Question 7.
H.O.T. Multi-Step Reasoning âˆ DRQ is a straight angle. The mâˆ DRB is twice the mâˆ QRT. What is the mâˆ DRB?

(A) 40Â°
(B) 150Â°
(C) 160Â°
(D) 220Â°
A.

Explanation:
Given that mâˆ DRQ is a straight angle which means mâˆ DRQ = 180Â° and mâˆ DRL = 75Â°, mâˆ LRT = 85Â° the equation will be
mâˆ DRQ = mâˆ DRL+mâˆ LRT+mâˆ QRT
180Â° = 75Â°+85Â°+âˆ QRT
180Â° = 160Â°+âˆ QRT
âˆ QRT = 180Â°-160Â°
= 20Â°.
As mâˆ DRB is twice the mâˆ QRT, so âˆ DRB is 2Ã—20Â° = 40Â°.

Question 8.
Which equation can you use to find the mâˆ XZW?

(A) 71Â° – 42Â° = __________
(B) 71Â° + 42Â° = __________
(C) 71Â° Ã— 42Â° = __________
(D) 180Â° – 113Â° = __________
B.

Explanation:
The equation will be
mâˆ XZW = mâˆ YZW+mâˆ XZY
=71Â° + 42Â°
= 113Â°.

Question 9.
Use Diagrams A sea turtle walks along a path that forms âˆ ABC. What is the measure of the angle formed by the path the turtle walked?

(A) 51Â°
(B) 12Â°
(C) 90Â°
(D) 89Â°
C.

Explanation:
The measure of the angle formed by the path the turtle walked is
âˆ ABC = 51Â°+39Â°
= 90Â°.

4th Grade Go Math Answer Key Join and Separate Angles Lesson 14.4 Question 10.
Use Diagrams What is the mâˆ DEF?

(A) 90Â°
(B) 73Â°
(C) 105Â°
(D) 98Â°
D.

Explanation:
The measure of the mâˆ DEF is
mâˆ DEF = 38Â°+25Â°+35Â°
= 98Â°.

Question 11.
Multi-Step Mike used a protractor to find the measure of each angle in the circle below. What is the mâˆ JLK?

(A) 360Â°
(B) 130Â°
(C) 230Â°
(D) 120Â°
C.

Explanation:
Given that mâˆ JLM is 102Â° and mâˆ KLM is 128Â° , so the measure of angle mâˆ JLK is 102Â°+128Â° which is 230Â°.

TEXAS Test Prep

Question 12.
Larry has 3 pieces of pie left. The measure of the angle of one piece is 35Â°. The second piece has an angle with a measure of 25Â°. The third piece has an angle with a measure that is half of the combined measures of the other two pieces. What is the total measure of the angle formed by all three pieces?
(A) 60Â°
(B) 90Â°
(C) 120Â°
(D) 180Â°
B.

Explanation:
Given that Larry has 3 pieces of pie left and the measure of the angle of one piece is 35Â° and the second piece has an angle with a measure of 25Â° by combing both we will get 35Â°+25Â° which is 60Â°. As the third piece has an angle with a measure that is half of the combined measures of the other two pieces, so the third piece is 60Â°Ã·2 which is 30Â°. So the total measure of the angle formed by all three pieces 60Â°+30Â° which is 90Â°.

### Texas Go Math Grade 4 Lesson 14.4 Homework and Practice Answer Key

Add to find the measure of the angle. Write an equation to record your work.

Question 1.

mâˆ PQR = __________
mâˆ PQR = 90Â°.

Explanation:
The measure of the angle mâˆ PQR is
mâˆ PQR = 75Â°+15Â°
= 90Â°.

mâˆ WXY = __________
mâˆ WXY = 175Â°.

Explanation:
The measure of the angle mâˆ WXY is
mâˆ WXY = 43Â°+39Â°+93Â°
= 175Â°.

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 3.

Question 4.

Problem Solving

Question 5.
Kenny drew and cut out an angle that measured 85Â°. Beginning at the vertex, he cut the angle into two angles. One of new angles measures 20Â°. What is the measure of the other new angle?
The measure of the other new angle is 65Â°.

Explanation:
Given that Kenny drew and cut out an angle that measured 85Â° and he cut the angle into two angles, so the measure of the new angle is 20Â°. So the measure of the other new angle is 85Â°-20Â° which is 65Â°.

Question 6.
Liam and Marcy each have slices of pizza. The measure of the angle of Liamâ€™s sLice is 40Â°. The measure of the angle of Marcyâ€™s slice is 35Â°. When the pieces are together, what is the measure of the angle they form?
The measure of the angle they form is 75Â°.

Explanation:
Given that the measure of the angle of Liamâ€™s slice is 40Â° and the measure of the angle of Marcyâ€™s slice is 35Â°. So the pieces together are 40Â°+35Â° which is 75Â°.

Lesson Check

Question 7.
Which equation can you use to find the m âˆ DEG?

(A) 67Â° + 90Â° = __________
(B) 67Â° Ã— 2 = __________
(C) 180Â° – 90Â°= __________
(D) 90Â° – 67Â° = __________
D.

Explanation:
As mâˆ DEF is 90Â° mâˆ GEF is 67Â° and the equation of mâˆ DEF = âˆ GEF+âˆ DEG, so âˆ DEG is
mâˆ DEF = âˆ GEF+âˆ DEG
90Â° = 67Â°+âˆ DEG
âˆ DEG = 90Â°-67Â°
= 23Â°.

Texas Go Math Grade 4 Lesson 14.4 Join and Separate Angles Question 8.
What is the m âˆ KJN?

(A) 100Â°
(B) 77Â°
(C) 90Â°
(D) 80Â°
D.

Explanation:
The measurement of mâˆ KJN is
mâˆ KJN = 23Â°+34Â°+43Â°
= 80Â°.

Question 9.
Hannah cut a pie into three equal parts. What is the measure of the angle of each of the parts of the pie?
(A) 30Â°
(B) 90Â°
(C) 100Â°
(D) 120Â°
D.

Explanation:
As pie is like a full circle, so the angle will be 360Â°. As Hannah cut a pie into three equal parts so the measure of the angle of each of the parts of the pie is 360Â°Ã·3 which is 120Â°.

Question 10.
Which equation can you use to find the m âˆ PQR?

(A) 73Â° – 57Â° = ___________
(B) 130Â° + 90Â° = ___________
(C) 73Â° + 57Â° = ___________
(D) 180Â° – 130Â° = ___________
mâˆ PQR = 130Â°.

Explanation:
The equation will be
mâˆ PQR = m âˆ PQS+mâˆ SQR
= 73Â° + 57Â°
= 130Â°.

Multi-Step Melissa used a protractor to find the measure of each angle in the circle below. What is the m âˆ WZY?

(A) 218Â°
(B) 142Â°
(C) 120Â°
(D) 238Â°