472,560 views
21 votes
21 votes
I am stuck on this problem because I don't know how to set it up with having inly one angle given.

I am stuck on this problem because I don't know how to set it up with having inly-example-1
User Minkle Garg
by
2.9k points

1 Answer

22 votes
22 votes
Answer:

m∠A = 112°

Step-by-step 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°