Mathematics
In cyclic quadrilateral ABCD, ∠DAC = 27°; ∠DBA = 50° and ∠ADB = 33°. Calculate :
(i) ∠DBC,
(ii) ∠DCB,
(iii) ∠CAB.
Answer
(i) We know that,
Angles in same segment are equal.
∠DBC = ∠DAC = 27°.
Hence, ∠DBC = 27°.
(ii) We know that,
Angles in same segment are equal.
∠ACB = ∠ADB = 33°.
and,
∠ACD = ∠ABD = 50°.
From figure,
⇒ ∠DCB = ∠ACD + ∠ACB = 50° + 33° = 83°.
Hence, ∠DCB = 83°.
(iii) In quad. ABCD,
⇒ ∠DAB + ∠DCB = 180° [As sum of opposite angles in a cyclic quadrilateral = 180°]
⇒ ∠DAC + ∠CAB + ∠DCB = 180°
⇒ 27° + 83° + ∠CAB = 180°
⇒ ∠CAB + 110° = 180°
⇒ ∠CAB = 180° - 110° = 70°.
Hence, ∠CAB = 70°.
Related Questions
In the figure given alongside, AOB is a diameter of the circle and ∠AOC = 110°, find ∠BDC.
In the figure given alongside, AB || CD and O is the center of the circle. If ∠ADC = 25°; find the angle AEB. Give reasons in support of your answer.
In the following figure, O is the centre of the circle, ∠AOB = 60° and ∠BDC = 100°. Find ∠OBC.
In the figure given alongside, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 80° and ∠CDE = 40°, find the number of degrees in :
(i) ∠DCE,
(ii) ∠ABC.
