Q25 of 141 Page 447

In the given figure, O is the centre of a circle and chords AC and BD intersect at E. If ∠AEB = 110° and ∠CBE = 30° then ∠ADB = ?

Given: ∠AEB = 110° and ∠CBE = 30°


∠AEC = ∠AEB + ∠BEC = 180°


∠AEB + ∠BEC = 180°


110° + ∠BEC = 180°


∠BEC = 180° – 110°


∠BEC = 70°


In ΔBEC


By angle sum property


∠CBE + ∠BEC + ∠ECB = 180°


30° + 70° + ∠ECB = 180°


∠ECB = 180° – 30° – 70°


∠ECB = 80°


Here,


∠ECB = ∠ADB (angles in the same segment)


∴ ∠ECB = ∠ADB = 80°


∴ ∠ADB = 80°

More from this chapter

All 141 →
23

In the given figure, O is the centre of a circle and ∠OAB = 50°. Then, ∠CDA = ?

 24

In the give figure, and are two intersecting chords of a circle. If ∠CAB = 40° and ∠BCD = 80°, then ∠CBD = ?

 26

In the given figure, O is the centre of a circle in which ∠OAB = 20° and ∠OCB = 50°. Then, ∠AOC = ?

 27

In the given figure, AOB is a diameter and ABCD is a cyclic quadrilateral. If ∠ADC = 120°, then ∠BAC = ?