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

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

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

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

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

Fill in the Blanks

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

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