Math help request

>>273755
Well it looks like a step-by-step solution is already in your image...
I can go more in depth I guess.

Line one in that image's solution:
Sides AD and DC are equal, as you can see from the circle. So this is an isoceles triangle, and angles CAD and ACD must be equal as well.
You know the 3 angles inside the triangle must add to 180. So CAD + ACD + 98 = 180, meaning both angles are 41 degrees.

Line two:
Because ABCD is a trapezoid, you know BAD + ADC = 180 (and ABC + BCD = 180).
Since you already know ADC = 98, you can find that BAD = 82 degrees.

Line three:
Since BAD = 82 degrees and CAD = 41 degrees, you know BAC = 82-41 = 41.

Line four.
Lines AB and AC are equal, so angles ABC and ACB are equal as well. You already know angle BAC, so you can solve to find beta = ABC = 69.5

>>273762
Thank you so much for your reply. I get it now to the most part thanks to your easy understandable explanation.

But one question still raises:

To find out BAD the solution says 180°-98°. But when I image a triangle BAD then I see that not the whole angle of D (delta) is in that triangle. So why taking 98°, the full angle of D? And why not substracting the angle of C (41°).

I hope you understood what I mean, Im not native... Thanks in advance :D

File: iamverysmart.png (167KB, 759x521px) Image search: [Google]

167KB, 759x521px

>>273755
done

>>273784
BAD is just the name of one angle, not a triangle.

Here, we're not looking at it as a triangle. We're looking at it as one of the 4 corners of the trapezoid/"trapez".

>>273878
Sorry I guess I look really stupid now but I still don't get it fully.

My problem: You say that to find BAD we look it as a trapezoid. Okay, but then why taking 180° like in triangles and not 360°. Because it would be logical to me to take 360° as the full figure has 4 corners.

And when we look: BAD=180°-98°=82°

Why not substracting the angle of BCD (41°) too?

>>274373

That's one of the important properties of a trapeziod. Two angles that are connected through a non parallel side are always 180°!
See

http://www.mathe-lexikon.at/geometrie/ebene-figuren/vierecke/trapez/winkel.html

>In einem Trapez verlaufen zwei gegenüberliegende Seiten parallel zueinander. Deshalb beträgt die Summe der beiden Winkel, die an einem Schenkel (= nicht parallele Seite) anliegen, immer 180°.

>>274378
Finally got it, thanks so much to everyone! :D