Question

In triangle ΔABC, ∠C is a right angle and CD is the altitude to AB . Find the measures of the angles of the ΔCBD and ΔCAD if: Chapter Reference a m∠A = 20°

Answer 1

1. ∆CBD: ∠B = 70°; ∠BCD = 20°; ∠ BDC = 90°

2. ∆CDA: ∠ACD = 70°; ∠A = 20°; ∠ ADC = 90°

Explanation:

1. ∆DBC

In ∆ABC

∠A + ∠B + ∠C = 180°

20° + ∠B + 90 ° = 180°

∠B + 110 ° = 180°

∠DBC = ∠B = 70°

In ∆CBD

∠BDC = 90°

∠B + ∠BCD + ∠CBD = 180°

70° + ∠BCD + 90 ° = 180°

∠BCD + 160° = 180°

BCD = 20°

2. ∆CAD

∠A + ∠ACD + ∠ADC = 180°

20° + ∠ACD + 90° = 180°

∠ACD + 110° = 180°

∠ACD = 70°