Question

Math help please!

Fill in the blanks in the proof. Don’t forget the missing angle in step 4. (1 points per blank)
Given x // t, m∠16=m∠7
Prove: k // w

Answer 1

x || t, [Given]

`m\angle 16 = m\angle 7` [Given] ......[1]

Transversal defined as a line that cuts across two or more Parallel lines.

When two parallel lines are cut by a transversal, then the pairs of corresponding angles are equal in measure.

`m\angle 16 = m\angle 1` [Corresponding Angle theorem] ......[2]

Substitute value [1] in [2] we have;

`m\angle 7 =m\angle 1` [Substitution Property]

When two lines are cut by a transversal and the alternate exterior angles are equal in measure, then the lines are parallel.

k || w [ By Alternative Exterior Angle Theorem] Hence proved!