In triangle ABC, angle A = 90 degrees, BD is the bisector of the triangle, angle ADB = 50 degrees

In triangle ABC, angle A = 90 degrees, BD is the bisector of the triangle, angle ADB = 50 degrees a) find the angles of the triangle BDC b) Compare the segments BD and CD

Find ∠ABD:
∠ABD = 180 ° – ∠BAD – ∠ADB = 180 ° – 90 ° – 50 ° = 40 °.
Since ВD is a bisector, ∠CBD = ∠ABD = 40 °.
The angles ∠ADB and ∠BDC are adjacent, which means that ∠BDC = 180 ° – ∠ADB = 180 ° – 50 ° = 130 °.
Find ∠BCD:
∠BCD = 180 ° – ∠CBD – ∠BDC = 180 ° – 40 ° – 130 ° = 10 °.
Since ∠CBD> ∠BCD, CD> BD.