Find the measure of the missing angle.
56

34 degrees

Step-by-step explanation:

angles on a straight line add up to 180 degrees so over here the middle angle as we can see is 90 degrees so we add that to the 56 degrees. From adding them we get 146. 180 -146 is 34 degrees and that is our answer. :)

a

step-by-step explanation:

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough