lines e and f are parallel. the m∠9 = 80° and m∠5 = 55°. which angle measures are correct? select three…

lines e and f are parallel. the m∠9 = 80° and m∠5 = 55°. which angle measures are correct? select three options. □m∠2 = 125° □m∠3 = 55° □m∠8 = 55° □m∠12 = 100° □m∠14 = 100°

lines e and f are parallel. the m∠9 = 80° and m∠5 = 55°. which angle measures are correct? select three options. □m∠2 = 125° □m∠3 = 55° □m∠8 = 55° □m∠12 = 100° □m∠14 = 100°

Answer

Explanation:

Step 1: Identify corresponding and alternate angles

Since lines ( e \parallel f ), ( \angle 5 ) and ( \angle 3 ) are alternate interior angles (截线 ( c )), so ( m\angle 3 = m\angle 5 = 55^\circ ) (Option B correct).

Step 2: Calculate supplementary angles for ( \angle 9 )

( \angle 9 = 80^\circ ), and ( \angle 9 ) is supplementary to ( \angle 10 ) (邻补角), so ( m\angle 10 = 180^\circ - 80^\circ = 100^\circ ). Since ( \angle 10 ) and ( \angle 12 ) are vertical angles (对顶角), ( m\angle 12 = 100^\circ ) (Option D correct).

Step 3: Calculate ( \angle 2 ) using linear pair

( \angle 1 ) and ( \angle 5 ) are corresponding angles (截线 ( c )), so ( m\angle 1 = 55^\circ ). ( \angle 1 ) and ( \angle 2 ) are supplementary (邻补角), so ( m\angle 2 = 180^\circ - 55^\circ = 125^\circ ) (Option A correct).

Answer:

A. ( m\angle 2 = 125^\circ ), B. ( m\angle 3 = 55^\circ ), D. ( m\angle 12 = 100^\circ )