Question

1. what kind of angle relationship is shown above?

corresponding angles
vertical angles
alternate interior
alternate exterior
consecutive interior
consecutive exterior

1. are these angles congruent, complementary, or supplementary?

congruent
complementary
supplementary
none of the above

1. solve for x

Explanation:

Step1: Identify angle - pair type

The angles shown are vertical angles as they are opposite each other when two lines intersect.

Step2: Determine angle - relationship property

Vertical angles are congruent.

Step3: Solve for x

Since vertical angles are congruent, we set up the equation \(6x + 11=77\).
Subtract 11 from both sides: \(6x=77 - 11\), so \(6x = 66\).
Divide both sides by 6: \(x=\frac{66}{6}=11\).

Answer:

1. Vertical Angles
2. Congruent
3. 11