Question

In the given figure, AB is the diameter of the circle. If m._DAE = 20° and m. BDC = 50°, find m. BED ​

Answer 1

Question:

In the given figure, AB is the diameter of the circle. If m∠DAE = 20° and m∠BDC = 50°, find m∠BED.

Answer:

Option d) 60°

∠BED is 60°

Explanation:

∠ADB is angle in a semicircle, so ∠ADB = 90°

∠ADB = ∠BDC + ∠ADC

∠BDC + ∠ADC = 90°

50° + ∠ADC = 90°

∠ADC = 90° - 50°

∠ADC = 40°

In ∆ AED,

∠DAE = 20°

∠ADC = ∠ADE = 40°

By angle sum property of triangle,

∠ADE + ∠DAE + ∠AED = 180°

40° + 20° + ∠AED = 180°

∠AED = 180° - 60°

∠AED = 120°

∠BED + ∠AED = 180° (AB is a straight line)

∠BED + 120° = 180°

∠BED = 180° - 120°

∠BED = 60°