Answer: Angle A = 34 degrees
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Explanation:
Check out the diagram below.
Segment BD cuts angle EBC in half
So the two smaller pieces DBC and DBE are congruent. Let's call them x.
Let's make y = angle EBA.
Note how the diagram shows the angles x, x, and y forming a straight angle. So we can say
x+x+y = 180
2x+y = 180
y = -2x+180
We'll use this later.
For now, focus on triangle DEB. Angle E is 90 degrees and angle B is x.
D+E+B = 180
28+90+x = 180
x+118 = 180
x = 180-118
x = 62
Which means
y = -2x+180
y = -2*62+180
y = -124+180
y = 56
Now focus on triangle BEA. We have B = 56, E = 90 and A = z
B+E+A = 180
56+90+z = 180
146+z = 180
z = 180-146
z = 34
which is the measure of angle A.
