In triangle δabc, ∠c is a right angle and cd is the height to ab, find the angles in δcbd and δcad if: m∠a = α m∠dbc = m∠dcb = m∠cdb = m∠acd = m∠adc =

Refer to the figure shown below.

Given:
m∠C = 90°, because ∠C is a right angle.
m∠D = 90°, because CD is the height to AB.
m∠A = α

Because the sum of angles in a triangle is 180°, therefore
m∠DBC + 90° + α = 180°
m∠DBC = 90° - α

Again, for the same reason,
m∠DCB + m∠DBC + 90° = 180°
m∠DCB + 90° - α + 90° = 180°
m∠DCB = α

For the same reason,
m∠ACD + 90° + α = 180°
m∠ACD = 90° - α

m∠ADC = 90° (by definition)
m∠CDB = 90° (by definition)

m∠DBC = 90° - α
m∠DCB = α
m∠CDB = 90°
m∠ACD = 90° - α
m∠ADC = 90°