Question

to the angle measure shown. 4 ∠1: _ ∠4: _ ∠7: ___

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and the $130^{\circ}$ angle are vertical angles. So $\angle1 = 130^{\circ}$.

Step2: Use corresponding - angle property

Corresponding angles are equal when two parallel lines are cut by a transversal. $\angle4$ and the $130^{\circ}$ angle are corresponding angles. So $\angle4=130^{\circ}$.

Step3: Use alternate - exterior - angle property

Alternate - exterior angles are equal when two parallel lines are cut by a transversal. $\angle7$ and the $130^{\circ}$ angle are alternate - exterior angles. So $\angle7 = 130^{\circ}$.

Answer:

$\angle1:130^{\circ}$
$\angle4:130^{\circ}$
$\angle7:130^{\circ}$