Question

In triangle ΔABC, ∠C is a right angle and segment CD is the height to segment AB . Find the angles in ΔCBD and ΔCAD if m∠A = 20°

m∠CDB =

m∠CBD =

m∠BCD =

m∠CDA =

m∠ CAD=

m∠ACD =

Answer 1

Explanation:

Draw a picture (like the image below).

Notice that triangles ABC and ACD both contain right angles, and both contain angle A (20°). Since angles of a triangle add up to 180°, that means their third angle must also be the same (70°).

Also notice that triangles ABC and CBD both contain right angles, and both contain angle B (70°). So their third angle must also be the same (20°).

Therefore:

m∠CDB = 90°

m∠CBD = 70°

m∠BCD = 20°

m∠CDA = 90°

m∠CAD = 20°

m∠ACD = 70°