In triangle δabc, ∠c is a right angle and c is the height to ab. find the angles in δcbd and δcad if: m∠a = 65°

m∠cdb =
m∠cbd =
m∠bcd =
m∠cda =
m∠cad=
m∠acd =

  m∠CDB = 90°

  m∠CBD = 25°

  m∠BCD = 65°

  m∠CDA = 90°

  m∠CAD = 65°

  m∠ACD = 25°

Step-by-step explanation:

All of the triangles are similar:

  ΔADC ~ ΔCDB ~ ΔACB

so corresponding angles will be congruent. Of course, the acute angles in a right triangle are complementary, so ∠B = 90° -65° = 25°. Since CD ⊥ AB, both of the angles at D are right angles, 90°.

In the figure, the angles that look like they're the same size are the same size.