In the given figure, ABCD is a rhombus. If ∠ACD = 40°, then x is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 50°
Two properties of a rhombus decide this: its opposite sides are parallel, and its diagonals cross at right angles.
AB is parallel to DC and AC cuts both, so \(\angle CAB=\angle ACD=40^\circ\) (alternate angles)
The diagonals meet at right angles, so \(\angle AOB=90^\circ\)
In triangle AOB, the angles add up to \(180^\circ\): \(x=180^\circ-90^\circ-40^\circ=50^\circ\)
