Question

solve for x

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 relationship

The angles $(59 - 2x)^{\circ}$ and $(64 - 3x)^{\circ}$ are vertical angles as they are opposite each other when two lines intersect.

Step2: Use vertical - angle property

Vertical angles are congruent. So, we set up the equation $59 - 2x=64 - 3x$.

Step3: Solve the equation for x

Add $3x$ to both sides: $59 - 2x+3x=64 - 3x+3x$, which simplifies to $59 + x=64$. Then subtract 59 from both sides: $x=64 - 59$.

Answer:

1. B. Vertical Angles
2. A. Congruent
3. $x = 5$