## Engage NY Eureka Math 4th Grade Module 4 Lesson 10 Answer Key

### Eureka Math Grade 4 Module 4 Lesson 10 Problem Set Answer Key

Write an equation, and solve for the measure of ∠x. Verify the measurement using a protractor.

Question 1.

∠CBA is a right angle.

45° + ________ = 90°

x° = __________

Answer:

The value of x is 45°.

Explanation:

Given that <CBA is a right angle and angle B is 45°, so the angle CBA= 90° which is 45°+x= 90°, so the value of x is

x°= 90° – 45°

= 45°

So the value of x° is 45°.

Question 2.

∠GFE is a right angle.

_______ + ________ = _________

x° = __________

Answer:

The value of x is 70°.

Explanation:

Given that <GFE is a right angle which is 90° and another angle is 20°, so the angle GFE= 90° which is 20°+x= 90°, so the value of x is x°= 90° – 20°

= 70°.

So the value of x° is 70°.

Question 3.

∠IJK is a straight angle

___________ + 70° = 180°

x° = ____________

Answer:

The value of x is 110°

Explanation:

Given that <IJK is a straight angle which is 180° and another angle is 70°, so the angle IJK= 180° which is 70°+x= 180°, so the value of x is

x°= 180° – 70°

= 110°.

So the value of x° is 110°.

Question 4.

∠MNO is a straight angle

_________ + _________ = __________

x° = ___________

Answer:

The value of x is 97°

Explanation:

Given that <MNO is a straight angle which is 180° and another angle is 83°, so the angle MNO= 180° which is 83°+x= 180°, so the value of x is

x°= 180° – 83°

= 97°.

So the value of x° is 97°.

Solve for the unknown angle measurements. Write an equation to solve.

Question 5.

Solve for the measurement of ∠TRU. ∠QRS is a straight angle.

Answer:

The value of <TRU is 144°.

Explanation:

Given that <QRS is a straight angle which is 180° and another angle is 36°, so the angle MNO= 180° which is 36°+x= 180°, so the value of x is

x°= 180° – 36°

= 144°.

So the value of <TRU is 144°.

Question 6.

Solve for the measurement of ∠ZYV. ∠XYZ is a straight angle.

Answer:

The value of <ZYV is 12°.

Explanation:

Given that <XYZ is a straight angle which is 180° and another two angle is 108°+60° which is 168°, so the angle XYZ= 180° which is 168°+x= 180°, so the value of x is

x°= 180° – 168°

= 12°.

So the angle ZYV is 12°.

Question 7.

In the following figure, ACDE ¡s a rectangle. Without using a protractor, determine the measurement of ∠DEB. Write an equation that could be used to solve the problem.

Answer:

The value of x° is 63°.

Explanation:

Here, in the above image we can see that a rectangle where every angle is a right angle, so let’s take one angle as 90° and then we should find out the other angle and the other angle be x. So the equation will be 90°= 27°+x° and the value of x is

x= 90° – 27°

= 63°.

So the value of x° is 63°.

Question 8.

Complete the following directions in the space to the right.

a. Draw 2 points: M and N. Using a straightedge, draw .

b. Plot a point O somewhere between points M and N.

c. Plot a point P, which is not on .

d. Draw \(\overline{O P}\).

e. Find the measure of ∠MOP and ∠NOP.

f. Write an equation to show that the angles add to the measure of a straight angle.

Answer:

The equation of the angles add to the measure of a straight angle is <MOP+<PON= 180°.

Explanation:

Here, we have plotted 2 points which are M and N using a straightedge, and have constructed .

Then we plotted a point O somewhere between points M and N.

Then we need to plot a point P, which is not on .

And now we will construct \(\overline{O P}\).

So, now we need to find the measure of ∠MOP and ∠NOP.

As we have plotted a straight line which is <MON is 180°, which is <MOP+<PON= 180°.

So the equation of the angles add to the measure of a straight angle is <MOP+<PON= 180°.

### Eureka Math Grade 4 Module 4 Lesson 10 Exit Ticket Answer Key

Write an equation, and solve for x. ∠TUV is a straight angle.

Equation = ______________

x° = ______________

Answer:

The value of x is 60°.

Explanation:

Given that <TUV is a straight angle which is 180° and another two angle is 53°+67° which is 120°, as the angle TUV= 180° which is 168°+x= 180°, so the value of x is

x°= 180° – 120°

= 60°.

So the angle x is 60°.

Write an equation, and solve for the measurement of ∠x. Verify the measurement using a protractor

Question 1.

∠DCB is a right angle

___________ + 35° = 90°

x° = ___________

Answer:

The value of x° is 55°.

Explanation:

Given that <DCB is a right angle and other angle is 35°, so the angle DCB is 90° which is 35°+x= 90°, so the value of x is

x°= 90° – 35°

= 55°

So the value of x° is 55°.

Question 2.

∠HGF is a right angle

___________ + ___________ = ___________

x° = ___________

Answer:

The value of x° is 28°.

Explanation:

Given that <HGF is a right angle and other angle is 62°, so the angle HGF is 90° which is 62°+x= 90°, so the value of x is

x°= 90° – 62°

= 28°

So the value of x° is 28°.

Question 3.

∠JKL is a straight angle.

145° + ___________ = 180°

x° = ___________

Answer:

The value of x is 35°.

Explanation:

Given that <JKL is a straight angle which is 180° and another angle is 145° and the angle JKL is 180° which is 145°+ x= 180°, so the value of x is

x°= 180° – 145°

= 35°.

So the angle x is 35°.

Question 4.

∠PQR is a straight angle.

___________ + ___________ = ___________

x° = ___________

Answer:

The value of x is 164°.

Explanation:

Given that <PQR is a straight angle which is 180° and another angle is 16° as the angle PQR is 180° which is 16°+x= 180°, so the value of x is

x°= 180° – 16°

= 164°.

So the angle x is 164°.

Write an equation, and solve for the unknown angle measurements.

Question 5.

Solve for the measurement of ∠USW. ∠RST is a straight angle.

Answer:

The value of x is 75°.

Explanation:

Given that <RST is a straight angle which is 180° and another two angle is 70°+35° which is 105°, as the angle RST= 180° and the equation is 105°+x= 180°, so the value of x is

x°= 180° – 105°

= 75°.

So the angle x is 75°.

Question 6.

Solve for the measurement of ∠OML. ∠LMN is a straight angle.

Answer:

The value of <OML is 35°.

Explanation:

Given that <LMN is a straight angle which is 180° and another two angle is 72°+73° which is 145°, as the angle LMN= 180° and the equation is 145°+x= 180°, so the value of x is

x°= 180° – 145°

= 35°.

So the angle <OML is 35°.

Question 7.

In the following figure, DEFH is a rectangle. Without using a protractor, determine the measurement of ∠GEF Write an equation that could be used to solve the problem.

Answer:

The value of x° is 16° and the equation is 90°= 74°+x°.

Explanation:

Here, in the above image we can see that a rectangle where every angle is a right angle, so let’s take one angle as 90° and then we should find out the other angle and the other angle be x. So the equation will be 90°= 74°+x° and the value of x is

x= 90° – 74°

= 16°.

So the value of x° is 16° and the equation is 90°= 74°+x°.

Question 8.

Complete the following directions in the space to the right.

a. Draw 2 points: Q and R. Using a straightedge, draw .

b. Plot a point S somewhere between points Q and R.

c. Plot a point T, which is not on

d. Draw \(\overline{T S}\).

e. Find the measure of ∠QST and ∠RST.

f. Write an equation to show that the angles add to the measure of a straight angle.

Answer:

The equation of the angles add to the measure of a straight angle is <QST+<STR= 180°.

Explanation:

Here, we need to draw 2 points which is Q and R using a straightedge and then we need to construct .

Then we need to plot a point S somewhere between points Q and R.

And then we need to plot a point T, which is not on

Then we will construct \(\overline{T S}\).

Then we need to find the measure of ∠QST and ∠RST.

As we have plotted a straight line which is <QSR is 180°, which is <QST+<STR= 180°.

So the equation of the angles add to the measure of a straight angle is <QST+<STR= 180°.