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

Given:

m∠C = 90°, because ∠C is a right angle.

m∠D = 90°, because CD is the height to AB.

m∠A = α

Since 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°

Step-by-step explanation:

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step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.