Question

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

Answer 1

Answer:

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

∘

.