1) We know that <DAB and <BAC are supplementary angles according to the exterior angle theorem, so we set up the following equation and solve:
105+x=180
x=75
2) Since we have the angles for <BAC and <ABC and a triangle has its total angles added up to 180, we can set up an equation to find <ABC and solve:
75+35+x=180
110+x=180
x=70
So the m<ABC is 70 degrees.
Hope this helped! Let me know if you need me to clarify anything.
Answer: Angle ABC is 70 degrees.
Step-by-step explanation:
We know that angle ACB is 35 degrees. We can also see in the picture that angle DAB and angle CAB are supplementary angles. Supplementary angles are 180 degrees so you can find CAB by subtracting 180 by 105(angle DAB is 105 degrees). So, CAB is 75 degrees. A triangle angles are always 180 degrees, so you can simply add angle CAB(75 degrees) and angle ACB(35 degrees), and subtract 180 from it:
35+75+?=180. ?= angle ABC
110+?=180
110-110+?=180-110
?=70
