Okay, here are the steps:
* Triangle ABC is an isosceles right triangle. This means angles A and C are equal.
* BD is the altitude drawn to the hypotenuse BC. This means BDE forms another right triangle with right angle at B.
* DE is the perpendicular bisector of BC. This means DE splits BC into two equal segments.
* Since BC is split into two equal segments, angles BDE and DBE must also be equal. We can call them both x.
* In the big triangle BDE:
- Angle at B is 90 degrees (right angle)
- One other angle is x (as discussed)
- Interior angles of a triangle sum to 180 degrees
So: 90 + x + x = 180
=> 2x = 90
=> x = 45
Therefore, the measures of the angles of triangle BDE are:
BDE = 45 degrees
DBE = 45 degrees
Angle at B (90 degrees)
Does this make sense? Let me know if you have any other questions!