Q:

PLEASE HELP WITH QUIZ!!!!!!!! 25 POINTS!!!!!!!!!!!!!Given a∥b , and c is not parallel to a or b, which statements must be true?Select each correct answer.m∠7=m∠10m∠4=m∠8m∠8=m∠9m∠2=m∠72.In this figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠3=120°.What is m∠6?wo supporting reasons are missing from the proof. Complete the proof by dragging and dropping the appropriate reasons into each of the empty boxes.Given: m∥nm∠1=120°Prove: m∠6=60°The figure shows what appear to be parallel lines n and m rising from left to right with line m above line n. Line p rises slightly from left to right first intersecting line n, then line m. The angles formed by the intersection of lines p and m are numbered from 1 through 4 in a clockwise direction starting with angle 1 which is located above line m and to the left of line p. The angles formed by the intersection of lines p and n are numbered 5 through 8 in a clockwise direction with angle 5 above line n and to the left of line p.Statements Reasons​ m∥nm∠1=120° ​ Given∠5≅∠1 m∠5=m∠1 Angle Congruence Postulatem∠5=120° Substitution Property of Equalitym∠6+m∠5=180° m∠6+120°=180° Substitution Property of Equalitym∠6=60° ​ Subtraction Property of Equality

Accepted Solution

A:
Answer:1. The correct options are 2 and 4.2. The measure of angle 6 is 60°.Step-by-step explanation:1.It is given that a∥b , and c is not parallel to a or b. So, we can not establish any relationship among the angles on the line a,b and  angles on the line c.If a traversal line intersect two parallel line, then corresponding angles, alternate exterior angle and alternate interior angles are equal.[tex]\angle 2=\angle 6=\angle 3=\angle 7[/tex][tex]\angle 1=\angle 5=\angle 4=\angle 8[/tex]Therefore  correct options are 2 and 4.2.It is given that AB∥CD and m∠3=120°.Statements                     Reasons ​ m∥nm∠1=120° ​                Given ∠5≅∠1                             Corresponding angles are equalm∠5=m∠1                    Angle Congruence Postulate m∠5=120°                    Substitution Property of Equality m∠6+m∠5=180°             Supplementary angle propertym∠6+120°=180°            Substitution Property of Equality m∠6=60° ​                    Subtraction Property of EqualityTherefore the measure of angle 6 is 60°.