Simple Geometry quiz

69

My head hurts already.  We know the total angle in the bottom left is the same as in the bottom right = 80.  Law of Sines or Law of Cosines should be used, I suppose.  This is assuming the base line is equal to the distance from the apex down the far right line to where the second apex occurs.

I'm going with 30 degrees.

42

Key to solving this is that 80 - 20 = 60.

BTW, 30 degrees is correct, by elementary geometry.

GB

Hmmm. Wouldn't 45 also be correct?

No it wouldn't. Rheumy old eyes didn't see the congruent segments.

Wouldn't 45 also be correct?

I draw it up in CAD and confirm that 30° is the answer.  Waiting for the simple geometry method. 

@norman-oklahoma

Start by drawing an equilateral triangle that includes the long side to the left.

Then recall the hint about 60 degrees.

GB