The diagonals of a rhombus ABCD intersect at the point O. If ∠BDC = 50°, then ∠OAB = ?
(a) 50°
(b) 40°
(c) 25°
(d) 20°

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Solution

(b) 40°

Explanation:
∠BDC = ∠ABD = 50^o (Alternate interior angles)
In ∆AOB, ∠ABD = 50^o and ∠AOB = 90^o
∴ ∠OAB = 180^o − (90^o + 50^o) = 40^o

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The diagonals of a rhombus ABCD intersect at the point O. If ∠BDC = 50°, then ∠OAB = ? (a) 50° (b) 40° (c) 25° (d) 20°

(b) ​40° Explanation: ∠BDC = ∠ABD = 50o (Alternate interior angles) In ∆AOB, ∠ABD = 50o and ∠AOB = 90o ∴ ∠OAB = 180o − (90o + 50o) = 40o

The diagonals of a rhombus ABCD intersect at the point O. If ∠BDC = 50°, then ∠OAB = ?
(a) 50°
(b) 40°
(c) 25°
(d) 20°

(b) 40°

Explanation:
∠BDC = ∠ABD = 50^o (Alternate interior angles)
In ∆AOB, ∠ABD = 50^o and ∠AOB = 90^o
∴ ∠OAB = 180^o − (90^o + 50^o) = 40^o