Question

A.B.C and D are 4 points on a circle.AC and BD intersect at a point E such that angle BEC = 130 degree and angle ECD = 20 degree,then angle BAC is

Answer 1

Answer:

110

Step-by-step explanation:

Here, ∠BEC+∠DEC=180

∘

(Linear pairs are complimentary)

⟹ 130

∘

+∠DEC=180

∘

⟹ ∠DEC=50

∘

.

In ΔDEC,

∠DEC+∠ECD+∠CDE=180

∘

...(Angle sum property)

⟹ 50

o

+20

o

+∠CDE=180

∘

⟹ ∠CDE=110

∘

.

By theorem of circles,

∠BAC=∠CDB

⟹ ∠BAC=∠CDE=110

o

∴∠BAC=110

∘

.