Question

10 points, answers needed for school so i dont fail ;)

Answer 1

Given: m ║ n, m∠1 = 50°, m∠2 = 48° and line bisects m∠ABC.

Prove: m∠3 = 49°

Since, m║n

And, , m∠1 = 50°, m∠2 = 48°

⇒m∠DEF = m∠1 + m∠2 = 50 + 48 = 98° ( By angle addition postulate)

Since, the alternative exterior angles made by the same transversal are congruent.

Therefore, m∠DEF = m∠ABC

⇒ m∠ABC= 98°

Since, line s bisects m∠ABC,

Therefore, By the definition of bisector,

m∠4 = m∠5

And, m∠4 = 1/2 × m∠ABC

⇒ m∠4 = 1/2 × 98°= 49°

But, m∠3 = m∠4 ( vertically opposite angles)

⇒ m∠3 = 49° ( by substituting the value of m∠4)

Answer 2

Explanation:

Given :

two parallel lines m and n.

Line s is bisector of angle ABC.

Angle DEF =98 degrees.

Angle DEF and ABC are exterior alternate angles for parallel lines.

Angle 3 is vertically opposite of angle 4

1. addition property of equality

2, alternate exterior

3. Definition of a bisector

4. Substitution property of equality