Question

Which angles have the same measure as $\angle 1$ in the diagram?

Short answer

The angles that have the same measure as $\angle 1$ are $\angle 4,\angle 5,\text{and}\angle 8$.

Step-by-step solution

Step 1. Given Information.

The provided figure is

Step 2. Concepts used.

Transversal and parallel lines

When two lines are crossed by another line, it is known as transversal. If two parallel lines are intersected by a transversal line then the corresponding angles are equal, alternate interior angles and alternate exterior angles are equal.

Step 3. Explanation.

Since vertically opposite angles are equal, $m\angle 1=m\angle 4$.

Since$\angle 1$ and $\angle 5$ are a pair of corresponding angles,$m\angle 1=m\angle 5$.

Since $\angle 1$ and $\angle 8$ are a pair of corresponding angles, $m\angle 1=m\angle 8$.

Step 4. Conclusion.

The angles that have the same measure as $\angle 1$ are $\angle 4,\angle 5,\text{and}\angle 8$.