Answer:
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)
