Exploring Vertical Angles in Geometry

What are opposite rays?

• Two rays that form a right angle

• Two collinear rays with a common endpoint extending in opposite directions

• Two rays that are parallel

• Two rays that intersect at a point

How do opposite rays appear in a diagram?

• As two intersecting lines

• As a single line with a common endpoint in the middle

• As a right angle

• As two parallel lines

Which of the following pairs are opposite rays in the given diagram?

• Ray EA and Ray ED

• Ray EB and Ray ED

• Ray EC and Ray ED

• Ray EA and Ray EC

What are vertical angles?

• Angles that are supplementary

• Angles that are adjacent

• Angles formed by two sets of opposite rays

• Angles that are complementary

Which angles are vertical angles in the given diagram?

• Angle 1 and Angle 3

• Angle 1 and Angle 2

• Angle 2 and Angle 3

• Angle 2 and Angle 4

What is the relationship between vertical angles and supplementary angles?

• Vertical angles are always supplementary

• Vertical angles are never congruent

• Vertical angles are always complementary

• If two angles are supplementary to the same angle, they are congruent

What can be concluded about vertical angles based on their relationship with supplementary angles?

• Vertical angles are never congruent

• Vertical angles are congruent

• Vertical angles are always complementary

• Vertical angles are always supplementary

In the example problem, what is the equation set up to find the value of x?

• 2x + 5 = x + 30

• x + 5 = 30

• 2x + 5 = 30

• x + 5 = 2x + 30

What is the value of x in the example problem?

• 35

• 30

• 25

• 20

What is the measure of angle 1 in the example problem?

• 65 degrees

• 60 degrees

• 55 degrees

• 50 degrees