So the angle AEC=90 degrees

Because angle AEC+ angle BAC+ angle ACE= 180 degrees.

Angle BAC=45 degrees

So the angle ACE=45 degrees

Because angle BCA= angle ACE+ angle BCE=75 degrees.

So the angle BCE=30 degrees

Because AD is perpendicular to BC and D.

So the angle MDC=90 degrees.

Because angle AMC= angle BCE+ angle MDC

So the angle AMC= 120 degrees.

2. Solution: Because the heights BD and CE of the triangle ABC intersect at the H point.

So ADH angle = AEH angle =90 degrees.

Because angle A+ angle ADH+ angle AEH+ angle DHE=360 degrees.

Angle A=85 degrees

So DHE angle =95 degrees

Because angle DHE= angle BHC

So the angle BHC=95 degrees

3, which means 1. Where is corner 2? Please draw a picture.

4. solution: because DE is perpendicular to AB and e.

So the angle bed =90 degrees.

Because angle bed+angle ABC+ angle D= 180 degrees.

So angle ABC+ angle D=90 degrees.

So angle D=90 degrees angle ABC

Because angle ABC= angle ACB

Because angle A+ angle ABC+ angle ACB= 180 degrees.

So angle A= 180-2 angle ABC.

1/2 Angle A=90 degrees Angle ABC

So angle A=2 angle d

5. Solution: Because A

a+b+c= 13

So (1) a= 1 b=6 c=6.

(2)a=2，b=5，c=6

(3) a=3 b=4 c=8

(4) a=3 b=c=5

(5)a=b=4 c=5

So there are five such triangles.

Please draw a picture.

7. Solution: (1) Because the angle C=90 degrees.

So the area of the triangle ABC = 1/2*AC*BC.

Because AC=5cm BC= 12cm.

So the area of the triangle ABC = 30cm 2.

Because CD is the height next to AB.

So the area of the triangle ABC = 1/2*AB*CD.

Because AB= 13cm.

So CD=60/ 13cm.