Question

Drag and drop an answer to each box to correctly complete the proof.

Given: m | n m 1 = 50 m 2 = 48°, and line s bisects ABC

Prove: m/3

49°

It is given that m | n m

1 = 50 m

2

- 48° and fine s bisects

ABC By the

m/DEF = 989 Because

angles formed by two parallel lines and a transversal are congruent

DEF

A BC

SO MZABC 98 By the

angles 4 and 5 are congruent

and m

4 is half m

ABC So the measure of in24_49 Because vertical angles

Answer 1

Explanation:

The correct question is shown in the image attached below.

Recall that: the line m is parallel to line n. In addition to that,
`m \angle 1 = 50^0` and
`m \angle 2 = 48^0`, and
`\angle ABC` is bisected by line s.

At this moment, by the angle addition postulate, angle DEF i.e.

∠DEF
`= m \angle 1 + m \angle 2`

∠DEF = 50° + 48°

∠DEF = 98°

Similarly, using the rule of the alternate exterior angle ∠DEF = ∠ABC (∵ alternate exterior angles exhibit congruency).

Furthermore, By the definition of a bisector, angles 4 and 5 are congruent due to the fact that the line of a bisector splits the angle into two equal parts.

m∠4 = m∠5

∴

98/2 = 49°

Finally;

from the diagram, angle 3 and 4 are vertical angles

Thus, m∠3 = 49 by substitution property of equality ( because vertical angles are congruent angles).