Answer:
m∠A = 112°
Explanation:
Given:
AB is parallel DC
DB bisects ∠ADC
m∠1 = 34°
To find:
m∠A
DB bisects ∠ADC
This means it divides ADC into two equal angles
∠ADC = ∠ADB + ∠BDC
∠ADB = ∠BDC
∠ADB = 1, ∠BDC = 2
Hence, 1 = 2
∠BDC = ∠ABD (alternate angles are equal)
∠BDC = 2, ∠ABD = 2
Sum of angles in triangle ABD:
∠ADB + ∠ABD + ∠DAB = 180° (sum of angles in a triangle)
1 + 3 + ∠DAB = 180
recal 3 = 2 and 2 = 1
34 + 34 + ∠DAB = 180
68 + ∠DAB = 180
∠DAB = 180 - 68
∠DAB = 112°
∠DAB = m∠A
m∠A = 112°
