Question

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 =

Answer 1

m∠CDB = 90°

m∠CBD = 25°

m∠BCD = 65°

m∠CDA = 90°

m∠CAD = 65°

m∠ACD = 25°

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.