Refer to our Texas Go Math Grade 4 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 4 Lesson 14.4 Answer Key Join and Separate Angles.

## 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?

Answer:

**Investigate**

Materials

- construction paper
- scissors
- protractor

A. Use construction paper. Draw an angle that measures exactly 70°. Label it ∠ABC.

Answer:

The measure of angle 70° is

B. Cut out ∠ABC.

Answer:

C. Form two new angles from ∠ABCby cutting it into two parts. Begin cutting at the vertex and cut between the rays.

What figures did you form? ____________

Answer:

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

Record the measures. ____________

Answer:

E. Find the sum of the angles you formed.

Answer:

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

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

Answer:

**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.

Answer:

**Math Talk**

Mathematical Processes

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

Answer:

**Share and Show**

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

Question 1.

m∠PQT = ____________

Answer:

m∠PQT = 80°.

Explanation:

The equation of m∠PQT is

m∠PQT = 43°+37°

= 80°.

Question 2.

m∠JKL = ______________

Answer:

m∠JKL = 100°.

Explanation:

The equation of m∠JKL is

m∠JKL = 90°+10°

= 100°.

Question 3.

m∠RHS = ______________

Answer:

m∠RHS = 160°,

Explanation:

The equation of m∠RHS is

m∠RHS = 55°+27°+78°

= 160°.

**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.

Answer:

m∠KLM = 160°,

m∠KLJ = 80°,

m∠LMJ = 120°.

Explanation:

By measuring each angle is

m∠KLM = 160°,

m∠KLJ = 80°,

m∠LMJ = 120°,

and the sum of the angle measures as an equation is 160°+80°+120° = 360°.

Question 5.

Answer:

m∠WVZ = 90°,

m∠YVZ = 90°,

m∠WVX = 140°,

m∠YVX = 40°.

Explanation:

By measuring each angle

m∠WVZ = 90°,

m∠YVZ = 90°,

m∠WVX = 140°,

m∠YVX = 40°,

and the sum of the angle measures as an equation is 90°+90°+140°+40° = 360°.

**Unlock the Problem**

Question 6.

**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 45°. When the pieces were together, what is the measure of the angle they formed?

(A) 90°

(B) 135°

(C) 180°

(D) 225°

Answer:

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 45°. So the measurement of the angle formed is 45°+45°+45° which is 135°.

a. What are you asked to find?

Answer:

Here, asked to find the measurement of the angle formed.

b. What information do you need to use?

Answer:

Here, we need information about the angle of each piece of pizza.

c. Justify Tell how you can use addition to solve the problem.

Answer:

Here, we have used addition to know the measurement of the pizza.

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

Answer:

Question 7.

**H.O.T. Multi-Step** Reasoning ∠DRQ is a straight angle. The m∠DRB is twice the m∠QRT. What is the m∠DRB?

(A) 40°

(B) 150°

(C) 160°

(D) 220°

Answer:

A.

Explanation:

Given that m∠DRQ is a straight angle which means m∠DRQ = 180° and m∠DRL = 75°, m∠LRT = 85° the equation will be

m∠DRQ = m∠DRL+m∠LRT+m∠QRT

180° = 75°+85°+∠QRT

180° = 160°+∠QRT

∠QRT = 180°-160°

= 20°.

As m∠DRB is twice the m∠QRT, so ∠DRB is 2×20° = 40°.

Question 8.

Which equation can you use to find the m∠XZW?

(A) 71° – 42° = __________

(B) 71° + 42° = __________

(C) 71° × 42° = __________

(D) 180° – 113° = __________

Answer:

B.

Explanation:

The equation will be

m∠XZW = m∠YZW+m∠XZY

=71° + 42°

= 113°.

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 9.

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

(A) 51°

(B) 12°

(C) 90°

(D) 89°

Answer:

C.

Explanation:

The measure of the angle formed by the path the turtle walked is

∠ABC = 51°+39°

= 90°.

Question 10.

Use Diagrams What is the m∠DEF?

(A) 90°

(B) 73°

(C) 105°

(D) 98°

Answer:

D.

Explanation:

The measure of the m∠DEF is

m∠DEF = 38°+25°+35°

= 98°.

Question 11.

**Multi-Step** Mike used a protractor to find the measure of each angle in the circle below. What is the m∠JLK?

(A) 360°

(B) 130°

(C) 230°

(D) 120°

Answer:

C.

Explanation:

Given that m∠JLM is 102° and m∠KLM is 128° , so the measure of angle m∠JLK is 102°+128° which is 230°.

**TEXAS Test Prep**

Question 12.

Larry has 3 pieces of pie left. The measure of the angle of one piece is 35°. The second piece has an angle with a measure of 25°. 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) 60°

(B) 90°

(C) 120°

(D) 180°

Answer:

B.

Explanation:

Given that Larry has 3 pieces of pie left and the measure of the angle of one piece is 35° and the second piece has an angle with a measure of 25° by combing both we will get 35°+25° which is 60°. 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 60°÷2 which is 30°. So the total measure of the angle formed by all three pieces 60°+30° which is 90°.

### 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.

m∠PQR = __________

Answer:

m∠PQR = 90°.

Explanation:

The measure of the angle m∠PQR is

m∠PQR = 75°+15°

= 90°.

Question 2.

m∠WXY = __________

Answer:

m∠WXY = 175°.

Explanation:

The measure of the angle m∠WXY is

m∠WXY = 43°+39°+93°

= 175°.

**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.

Answer:

Question 4.

Answer:

**Problem Solving**

Question 5.

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

Answer:

The measure of the other new angle is 65°.

Explanation:

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

Question 6.

Liam and Marcy each have slices of pizza. The measure of the angle of Liam’s sLice is 40°. The measure of the angle of Marcy’s slice is 35°. When the pieces are together, what is the measure of the angle they form?

Answer:

The measure of the angle they form is 75°.

Explanation:

Given that the measure of the angle of Liam’s slice is 40° and the measure of the angle of Marcy’s slice is 35°. So the pieces together are 40°+35° which is 75°.

**Lesson Check**

**Fill in the bubble completely to show your answer.**

Question 7.

Which equation can you use to find the m ∠DEG?

(A) 67° + 90° = __________

(B) 67° × 2 = __________

(C) 180° – 90°= __________

(D) 90° – 67° = __________

Answer:

D.

Explanation:

As m∠DEF is 90° and m∠GEF is 67° and the equation of m∠DEF = ∠GEF+∠DEG, so ∠DEG is

m∠DEF = ∠GEF+∠DEG

90° = 67°+∠DEG

∠DEG = 90°-67°

= 23°.

Question 8.

What is the m ∠KJN?

(A) 100°

(B) 77°

(C) 90°

(D) 80°

Answer:

D.

Explanation:

The measurement of m∠KJN is

m∠KJN = 23°+34°+43°

= 80°.

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) 30°

(B) 90°

(C) 100°

(D) 120°

Answer:

D.

Explanation:

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

Question 10.

Which equation can you use to find the m ∠PQR?

(A) 73° – 57° = ___________

(B) 130° + 90° = ___________

(C) 73° + 57° = ___________

(D) 180° – 130° = ___________

Answer:

m∠PQR = 130°.

Explanation:

The equation will be

m∠PQR = m ∠PQS+m∠SQR

= 73° + 57°

= 130°.

Question 11.

**Multi-Step** Melissa used a protractor to find the measure of each angle in the circle below. What ¡s the m ∠WZY?

(A) 218°

(B) 142°

(C) 120°

(D) 238°

Answer:

Question 12.

**Multi-Step** Angle BAEis a straight angle. Them m∠FAE is half the m ∠BAC. What is the m∠FAE?

(A) 40°

(B) 80°

(C) 100°

(D) 30°

Answer: