All the solutions provided inÂ **McGraw Hill My Math Grade 4 Answer Key PDF Chapter 14 Lesson 7 Solve Problems with Angles **will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 4 Answer Key Chapter 14 Lesson 7 Solve Problems with Angles

An angle can be decomposed, or broken, into non-overlapping parts. The angle measure of the whole is the sum of the angle measures of the parts.

**Math in My World**

**Example 1**

Rachel and Dean made a sign out of fabric like the one shown to hang in the school gymnasium. The blue piece has a 35Â° Angle. The red piece is attached to the longest side of the blue piece. Together. the pieces form a right angle. What is the angle shown on the red piece?

One Way: Make a model.

Draw a 90Â° angle. Mark off a 35Â° angle. Measure the other angle.

The other angle has a measure of ____________.

Answer: 55 degrees

Another Way: Use an equation.

The 90Â° angle measure is the sum of two parts. One angle is 35Â°. Find the unknown angle measure.

Let r represent the unknown angle measure.

35 + r = 90

r = 90 – 35

r = ______________

So, the angle shown on the red piece measures _____________.

Answer: 55 degrees

**Example 2**

Find the combined measure of the angle shown.

One of the angles is 20Â°. The symbol on the other angle shows that it is a right angle. Therefore, it is 90Â°.

To find the combined measure of the angle, add the angle measures of the parts.

Let a represent the combined angle measure.

a = 20Â° + 90Â°

a = ______________

So, the combined measure of the angle is _______________.

Answer:

a = 20Â° + 90Â°

a = 110Â°

So, the combined measure of the angle is 110 degrees

**Guided Practice**

**Algebra **Find each unknown.

Question 1.

The combined angle measure is 90Â°.

n = ______________

Answer: 15 degrees

The 90Â° angle measure is the sum of two parts. One angle is 75Â°.

Let n represent the unknown angle measure.

75 + n = 90

n= 90 – 75 = 15 degrees

Question 2.

The combined angle measure is 130Â°.

k = ______________

Answer: 95 degrees

The 130Â° angle measure is the sum of two parts. One angle is 35Â°.

Let k represent the unknown angle measure.

k + 35 = 130

k = 130 – 35 = 95 degrees

Question 3.

Find the combined angle measure.

combined measure = _____________

Answer:Â 60 degrees

To find the combined measure of the angle, add the angle measures of the parts.

Let a represent the combined angle measure.

a = 25Â° + 35Â°

a = 60 degrees

**Talk Math**

How can the measures of parts of an angle be used to find the combined measure?

Answer: Combined measure is possible with adjacent angles. Two angles that are next to each other without overlapping are called Adjacent angles. These angles can be added together to make a larger angle. In order to get the combined measure of an angle, calculate the individual angles and simply perform addition. Adding angles is the same as adding numbers. We can add two or more angles as long as they are not overlapping.

**Independent Practice**

**Algebra Find each unknown.**

Question 4.

The combined angle measure is 50Â°.

a = ______________

Answer: 20 degrees

The combined angle measure is 50Â°. The 50Â° angle measure is the sum of two parts. One angle is 30Â°.

Let a represent the unknown angle measure.

a + 30 = 50

a = 50 – 30 = 20 degrees

Question 5.

The combined angle measure is 90Â°.

n = _______________

Answer: 20 degrees

The combined angle measure is 90Â°. The 90Â° angle measure is the sum of two parts. One angle is 70Â°.

Let n represent the unknown angle measure.

n + 70 = 90

n = 90 – 70 = 20 degrees

Question 6.

The combined angle measure is 125Â°.

g = ________________

Answer: 50 degrees

The combined angle measure is 125Â°. The 125Â° angle measure is the sum of two parts. One angle is 75Â°.

Let g represent the unknown angle measure.

g + 75 = 125

g = 125 – 75 = 50 degrees

Question 7.

The combined angle measure is 150Â°.

s = ________________

Answer: 60 degrees

The combined angle measure is 150Â°. The 150Â° angle measure is the sum of two parts. One angle is 90Â°.

Let s represent the unknown angle measure.

s + 90 = 150

s = 150 – 90 = 60 degrees

Question 8.

Draw a triangle with one right angle.

Find the combined measure of the three angles.

Answer:

For any triangle, the sum of all the interior angles is equal toÂ 180 degrees. For a right angle triangle, one of the angle is 90 degrees. So the combined angle of other two angles is 180 – 90 = 90 degrees.

Question 9.

Draw a triangle with one obtuse angle.

Find the combined measure of the three angles.

Answer:

For any triangle, the sum of all the interior angles is equal to 180 degrees. To draw an obtuse angle triangle, we choose 120 degrees as one of the angles in the triangle. So the combined angle of other two angles is 180 – 120 = 60 degrees.

**Problem Solving**

Question 10.

The steps on a staircase should be 90Â°. One of the steps is crooked. The angle formed is 15Â° too large. What is the angle of that step?

Answer: 105 degrees

The steps on a staircase should be 90Â°.

The angle formed by the crooked step is 15 degrees more.

Therefore, the angle of that crooked step = 90 + 15 = 105 degrees.

Question 11.

**Mathematical PRACTICE** Model Math The combined measure of the angles is 150Â°. One angle measures 50Â°. Find the value of x.

Answer: 100 degrees

The combined angle measure is 150Â°. The 150Â° angle measure is the sum of two parts. One angle is 50Â°.

Let x represent the unknown angle measure.

x + 50 = 150

x = 150 – 50 = 100 degrees

**HOT Problems**

Question 12.

**Mathematical PRACTICE** Understand Symbols Find the value of k.

k = ______________

Answer:Â 30 degrees

The combined angle measure is 90Â°, as the figure is right angle. 2k and k are both angles used to form 90 degrees

Therefore, 2k + k = 90

3k = 90

k = 30 degrees

Question 13.

**Building on the Essential Question** How is addition related to angle measurement?

Answer: Two angles that are next to each other without overlapping are called Adjacent angles.Â These angles can be added together to make a larger angle. Adding angles is the same as adding numbers. We can add two or more angles as long as they are not overlapping.

### McGraw Hill My Math Grade 4 Chapter 14 Lesson 7 My Homework Answer Key

**Practice**

**Algebra **Find each unknown.

Question 1.

The combined angle measure is 50Â°.

h = _____________

Answer: 35 degrees

The combined angle measure is 50Â°. The 50Â° angle measure is the sum of two parts. One angle is 15Â°.

Let h represent the unknown angle measure.

h + 15 = 50

h = 50 – 15 = 35 degrees

Question 2.

The combined angle measure is 135Â°.

p = _______________

Answer: 50 degrees

The combined angle measure is 135Â°. The 135Â° angle measure is the sum of two parts. One angle is 85Â°.

Let p represent the unknown angle measure.

p + 85 = 135

p = 135 – 85 = 50 degrees

Question 3.

The combined angle measure is 70Â°.

f = _________________

Answer: 25 degrees

The combined angle measure is 70Â°. The 70Â° angle measure is the sum of two parts. One angle is 45Â°.

Let f represent the unknown angle measure.

f + 45 = 70

f = 70 – 45 = 25 degrees

Question 4.

The combined angle measure is 115Â°.

t = _________________

Answer: 25 degrees

The combined angle measure is 115Â°. The 115Â° angle measure is the sum of two parts. One angle is 90Â°.

Let t represent the unknown angle measure.

t + 90 = 115

t = 115 – 90 = 25 degrees

Question 5.

The combined angle measure is 180Â°.

x = _________________

Answer: 30 degrees

The combined angle measure is 180Â°. The 180Â° angle measure is the sum of two parts. One angle is 150Â°.

Let x represent the unknown angle measure.

x + 150 = 180

x = 180 – 150 = 30 degrees

Question 6.

Find the value of r.

r = _________________

Answer: 55 degrees

The combined angle measure is 90Â°. The 90Â° angle measure is the sum of two parts. One angle is 35Â°.

Let r represent the unknown angle measure.

r + 35 = 90

r = 90 – 35 = 55 degrees

**Problem Solving**

Question 7.

**Mathematical PRACTICE** Make a Plan Suppose you draw a line from the center of a clock face to the number 12. When the minute hand gets to 3 on the clock face, the line and minute hand form a 90Â° angle. What angle does the line and the minute hand make when the minute hand is on 2?

Answer: 55 degrees

When hour and minute hand are at 12 and 2, then the time showing is 12:10

A clock is shaped like a circle and is composed of 360 degrees.

There are 60 minutes in an hour, and 360 degrees divided by 60 minutes is 6. Therefore, the minute hand moves 6 degrees per minute.

It takes 720 minutes for the hour hand to move around the clock. 360 degrees divided by 720 minutes is 0.5. Therefore, the hour hand moves 0.5 degrees per minute.

At 12:10, the hour hand has moved 10 out of 720 possible times from the top of the clock. 10 times 0.5 degrees is 5 degrees.

At 12:10, the minute hand has moved 10 out of 60 possible times from the top of the clock. 10 times 6 degrees is 60 degrees.

60-5 = 55 degrees

**Test Practice**

Question 8.

The combined angle measure is 120Â°. What is the value of n?

(A) 45

(B) 40

(C) 35

(D) 30

Answer: B (40)

The combined angle measure is 120Â°. The 120Â° angle measure is the sum of two parts. One angle is 80Â°.

Let k represent the unknown angle measure.

k + 80 = 120

k = 120 – 80 = 40 degrees