Finding Missing Angles Using Equations

Angles - Geometric Problems with Expression & Equations

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Common Angles

• Straight angles (or lines) are 180 degrees

• Right angles (perfect corner) are 90 degrees

• Obtuse angles are greater than 90 degrees

• Acute angles are less than 90 degrees

Multiple Choice

Identify the type of angle shown.

• acute

• obtuse

• right

• straight

Multiple Choice

Identify the type of angle shown.

• acute

• obtuse

• right

• straight

Multiple Choice

Identify the type of angle shown.

• acute

• obtuse

• right

• straight

Multiple Choice

Identify the type of angle shown.

• acute

• obtuse

• right

• straight

Multiple Choice

 

An angle is acute. It measures -6x + 108. Which inequality could be used to find the value of x?

 

• $$-6x+108\ge90$$  

• $$-6x+108\le90$$  

• $$-6x+108>90$$  

• $$-6x+108<90$$  

Multiple Choice

An angle is acute. It measures -6x + 108. What is the value of x?

• x > -3

• x < -3

• x > 3

• x < 3

Multiple Choice

An angle is obtuse.  It measures 6x - 8. 

What inequality could be used to find the value of x?

• 6x - 8 < 90

• 6x - 8 > 90

• 6x - 8 = 90

Vertical angles

• Vertical angles are angles directly across from each other that form when 2 lines intersect

• Vertical angles are congruent (equivalent in size/shape/measure)

Fill in the Blanks

What is the measure of angle y?

Multiple Choice

Which equation can be used to find the value of x?

• x + 7 + 100 = 180

• x + 7 = 100

• x + 7 + 100 = 90

• x + 7 + 90 = 100

Fill in the Blanks

What is the value of x?

Adjacent Angles

• Adjacent angles are two angles that have a common vertex and a common side but do not overlap (adjacent means "beside")

• There are 2 main kinds of adjacent angles:

• Supplementary angles - form a straight line (sum = 180 degrees)

• Complementary angles - form a right angle (sum = 90 degrees)

Multiple Choice

What is the relationship between the 2 angles shown?

• Complementary

• Supplementary

• Adjacent, but not complementary or supplementary

• vertical

Multiple Choice

What is the relationship between the 2 angles shown?

• complementary angles

• supplementary angles

• adjacent but not complementary or supplementary

• vertical

Multiple Choice

What is the relationship between the 2 angles shown?

• complementary

• supplementary

• adjacent but not complementary or supplementary

• vertical

Multiple Choice

What is the relationship between the 2 angles below?

• complementary

• supplementary

• adjacent, but not complementary or supplementary

• vertical

Multiple Choice

The following angles are complementary. What is the measure of angle GHI?

• 56 degrees

• 64 degrees

• 146 degrees

• 156 degrees

Fill in the Blanks

The following angles are complementary. What is the measure of angle x?

Multiple Choice

The following angles are complementary. Which equation can be used to find the measure of angle x?

• 2x = 90

• 3x = 180

• 2x + x = 90

• 2x + x = 180

Multiple Choice

The following angles are complementary. What are the measures of the 2 angles?

• 45 and 45

• 30 and 60

• 60 and 60

• 60 and 120

• 60 and 90

Multiple Choice

The following angles are complementary. What equation can be used to find the measure of the angle (by first finding the value of x)?

• 3x + 11 = 90

• 3x - 11 = 180

• 3x - 3 = 90

• 3x + 3 = 180

Fill in the Blanks

What is the value of x?

Multiple Choice

What are the measures of the 2 angles?

• 31 and 62

• 31 and 35

• 35 and 55

• 31 and 55

Multiple Choice

The following angles are supplementary. What is the measure of angle x?

• 28 degrees

• 62 degrees

• 180

Multiple Choice

The following angles are supplementary. Write an equation to find the value of x.

• 3x = 54

• 3x + 54 = 90

• 3x + 54 = 180

Fill in the Blanks

What is the value of x?

Fill in the Blanks

What is the measure of the missing angle?

Multiple Choice

Which equation could be used to find the measure of the angles?

• 2x + 3 = x - 6

• 2x + 3 = 180

• 3x + 9 = 90

• 3x - 3 = 180

Fill in the Blanks

What is the value of x?

Multiple Choice

What are the measures of the 2 angles?

• 61 and 180

• 125 and 55

• 61 and 29

• 61 and 119

Multiple Choice

Which equation can be used to find the value of x?

• 5x + 2x + 24 = 180

• 5x + 2x + 24 = 100

• 5x + 2x + 24 = 90

• 5x = 2x + 24

Fill in the Blanks

What is the value of x?