We included **HMH Into Math Grade 4 Answer Key PDF** **Module 13 Lesson 7 Find Unknown Angle Measures **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 13 Lesson 7 Answer Key Find Unknown Angle Measures

I Can use the relationship between known angles to find the measures of unknown angles.

**Step It Out**

Question 1.

A laptop’s screen size is usually measured by the length of its diagonal, which is the distance between opposite corners.

A. Look at the angles formed by the diagonal. Find ∠ABC. What do you notice about ∠ABC?

Answer:

∠ABC = 90°

Explanation:

∠ABC = ∠ABD +∠DBC

∠ABC = 90°

∠DBC = ∠ABC – ∠ABD = 90° – 61° = 29°

B. Circle all of the angle measure(s) that are known. Draw a line under the angle measure(s) that are unknown.

m∠ABC

m∠ABD

m∠DBC

Answer:

Explanation:

Given,

∠ABC = 90°

∠ABD = 61°

∠DBC = is un known

C. What kind of angle is ∠ABC?

Answer:

Right angle

∠ABC = 90°

Explanation:

Right angle is an angle exactly that measures 90°

D. Name two ways you can find the measure of ∠DBC.

Answer:

∠ABC = ∠ABD +∠DBC

∠ABC = 90°

∠DBC = ∠ABC – ∠ABD = 90° – 61° = 29°

another way is

x = 90° – 61° = 29°

Explanation:

If two angles are known we can find the unknown angle.

As we know the sum of angles in triangle is 180°

Turn and Talk How can you use the known angle measures to check if your measurement makes sense?

Answer:

An angle measure can be defined as the measure of the angle formed by the two rays.

Angles are measured in degrees using a protractor.

Question 2.

A tile-setter wants to cut another piece off of a tile. They need to know the measure of the unknown angle, labeled x, to determine the cut.

A. Estimate the unknown measure x.

Answer:

105°

Explanation:

Let the unknown angle be x

x = 225° – 120° = 105°

y= 360° – 225° = 135°

B. What information do you know?

Answer:

complete angle in the circle is 360°

and one angle is 120°

C. How can you use the information you know to solve for the unknown measure x?

Answer:

complete angle in the circle is 360°

and one angle is 120°

Explanation:

Let the unknown angle be x

x = 225° – 120° = 105°

D. Write an equation to model the value of x.

Answer:

105°

Explanation:

Let the unknown angle be x

x = 225° – 120° = 105°

E. Is your answer reasonable? How do you know?

Answer:

Yes, its reasonable

Explanation:

complete angle in the circle is 360°

and one angle is 120°

**Turn and Talk** The tile-setter already removed the piece of tile with an angle measure of y. How can you find the value of y?

Answer:

135°

Explanation:

complete angle in the circle is 360°

and one angle is 120°

y= 360° – 225° = 135°

**Check Understanding**

Question 1.

What kind of angle is ∠AED?

Answer:

Straight angle

Explanation:

Angle of straight angle is 180°

∠AED = ∠CED + ∠AEC

Given ∠CED = 45°, ∠AED = 180°

∠AEC = 180° – 45° + 135°

So, 45° + 135° = 180°

Question 2.

What is the measure of ∠AEC?

m∠AEC = ________

Answer:

m∠AEC = 135°

Explanation:

∠AED = ∠CED + ∠AEC

180° = 45° + ∠AEC

∠AEC = 180° – 45° = 135°

**On Your Own**

Question 3.

This is a diagram of the board that Susie cuts for a shelf.

Write an equation to find the measure of ∠VXY.

Answer:

30°

Explanation:

∠VXY = ∠WXY – ∠WXV

m∠VXY = 90° – 60° = 30°

Question 4.

Mark cut a piece of paper to make a bird. The directions he follows say for him to cut away an angle, so that he is left with an angle that measures 276°. What is the measure of the angle he must cut away?

Answer:

84°

Explanation:

Complete angle of a circle is 360°

left with an angle that measures 276°.

Let the unknown angle be x

360° – 276° = 84°

Question 5.

Now, Mark has to use the piece that he cut away to make wings for the bird. The directions say to cut the angle in half. What is the measure of each half of the cut-away angle?

Answer:

180°

Explanation:

Complete angle of a circle is 360°

Half of an angle that measures 180°.

Let the unknown angle be x

360° – 180° = 180°

Question 6.

How did you find the answer for Problem 5?

Answer:

180°

Explanation:

As we know total internal angle is 360° and the half of the 360° is 180

360° – 180° = 180°

**Write an equation to find the measure of the unknown angle.**

Question 7.

Answer:

45°

Explanation:

Let the unknown angle is x

x° = 130° – 85° = 45°

Angle less than 90° is acute angle.

Question 8.

Answer:

95°

Explanation:

Let the unknown angle be x

x° = 50° + 45° = 95°

Angle more than 90° is obtuse angle.

Question 9.

Answer:

80°

Explanation:

Let the unknown number be x

x° = 200° – 120° = 80°

Angle less than 90° is acute angle.

Question 10.

**Critique Reasoning** Ben said that when you separate a 90° angle into two angles, the new angles always measure 45°? How do you know if his statement is true or false?

Answer:

45°

Explanation:

Total angle of right angle is 90°

Half of right angle is 45°

90° – 45° = 45°

Question 11.

**Open Ended** Write an unknown angle measurement problem. Draw a diagram to help a classmate solve the problem.

Answer:

Mark cut a piece of paper to make a bird. The directions he follows say for him to cut away an angle, so that he is left with an angle that measures 60°. What is the measure of the angle he must cut away?

Explanation:

Let the unknown angle be x

90° – 60° = 30°

Question 12.

What is the unknown measure of q?

How do you know?

Answer:

90°

Explanation:

Angle of complete circle = 360°

Circle is divided in to 4 equal parts of 90° each.

360° – 270° = 90°