Question

lines ( ell ) and ( m ) are intersected by transversal ( t ) and ( ell parallel m ).

select all of the angles that are congruent to ( angle 5 ).

a. ( angle 1 )
b. ( angle 2 )
c. ( angle 3 )
d. ( angle 4 )
e. ( angle 7 )
f. ( angle 8 )

Explanation:

Step1: Use vertical angles property

Vertical angles are congruent. So, $\angle5\cong\angle7$.

Step2: Use alternate interior angles property (since $\ell\parallel m$)

Alternate interior angles are congruent. $\angle5\cong\angle4$.

Step3: Use corresponding angles property (since $\ell\parallel m$)

Corresponding angles are congruent. $\angle5\cong\angle1$.

Step4: Use transitive property (for $\angle2$)

$\angle2\cong\angle4$ (vertical angles), and since $\angle4\cong\angle5$, then $\angle2\cong\angle5$.

Answer:

A. $\angle1$, B. $\angle2$, D. $\angle4$, E. $\angle7$