The diagonals of a rectangle ABCD intersect at the point O. If ∠BOC = 50°, then ∠OAD = ?
(a) 50°
(b) 55°
(c) 65°
(d) 75°

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Solution

(c) 65°

Explanation:
∠BOC = 50° = ∠AOD (Vertically opposite angles)
In ∆ AOD, OA = OD (Diagonals are equal, so bisectors are also equal)
∴ ∠OAD = ∠ODA = $\frac{1}{2} (180 ° - 50 °) = 65 °$

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The diagonals of a rectangle ABCD intersect at the point O. If ∠BOC = 50°, then ∠OAD = ? (a) 50° (b) 55° (c) 65° (d) 75°

(c)​ 65° Explanation: ∠BOC = 50° = ​∠AOD (Vertically opposite angles) In ∆ AOD, OA = OD (Diagonals are equal, so bisectors are also equal) ∴ ​∠OAD = ​∠ODA = 12180°-50°=65°

The diagonals of a rectangle ABCD intersect at the point O. If ∠BOC = 50°, then ∠OAD = ?
(a) 50°
(b) 55°
(c) 65°
(d) 75°

(c) 65°

Explanation:
∠BOC = 50° = ∠AOD (Vertically opposite angles)
In ∆ AOD, OA = OD (Diagonals are equal, so bisectors are also equal)
∴ ∠OAD = ∠ODA = $\frac{1}{2} (180 ° - 50 °) = 65 °$