Mathematics
In the adjoining figure, ∠BEC = 125° and ∠ACD = 25°; then the angle BAC is :
100°
110°
90°
65°
Answer
From figure,
⇒ ∠BEC + ∠DEC = 180° (Linear pairs)
⇒ 125° + ∠DEC = 180°
⇒ ∠DEC = 180° - 125° = 55°.
In △DEC,
⇒ ∠DEC + ∠ECD + ∠CDE = 180°
⇒ 55° + 25° + ∠CDE = 180°
⇒ ∠CDE = 180° - 55° - 25° = 100°.
From figure,
∠BDC = ∠CDE = 100°
We know that,
Angles subtended by same segment of the circle are equal.
∴ ∠BAC = ∠BDC = 100°.
Hence, Option 1 is the correct option.
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