Question

5. In Fig. 10.39, A, B, C and D are four points on a
circle. AC and BD intersect at a point E such
that Z BEC = 130° and Z ECD = 20°. Find
BAC.​

Answer 1

Answer:

30°

Step-by-step explanation:

angle in same segment are equal.

Answer 2

Given :

∠BEC = 130°

∠ECD = 20°

To find :

∠BAC

Solution :

Since AC is a straight line

∠AEB + ∠BEC = 180°

∠AEB + 130° = 180° [ linear pair ]

∠AEB = 180° - 130°

∠AEB = 50°

∠DEC = ∠AEB = 50° [ vertically opp. angles]

In ∆DEC,

∠DEC + ∠ECD + ∠BDC = 180° [ angle sum property ]

50° + 20° + ∠BDC = 180°

70° + ∠BDC = 180°

∠BDC = 180° - 70°

∠BDC = 110°

Therefore, ∠BAC = ∠BDC = 110° [ anglea in the same segment are equal ]

Answer 3

Given :

∠BEC = 130°

∠ECD = 20°

To find :

∠BAC

Solution :

Since AC is a straight line

∠AEB + ∠BEC = 180°

∠AEB + 130° = 180° [ linear pair ]

∠AEB = 180° - 130°

∠AEB = 50°

∠DEC = ∠AEB = 50° [ vertically opp. angles]

In ∆DEC,

∠DEC + ∠ECD + ∠BDC = 180° [ angle sum property ]

50° + 20° + ∠BDC = 180°

70° + ∠BDC = 180°

∠BDC = 180° - 70°

∠BDC = 110°

Therefore, ∠BAC = ∠BDC = 110° [ anglea in the same segment are equal ]