In the given figure ABCD is a rhombus, the value of \(x\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 50°
In a rhombus each diagonal bisects the angles at the corners it joins, and adjacent angles add up to 180° (AB is parallel to DC). The angle \(x\) is half of the angle at D.
AC bisects angle A, so \(\angle DAC=\angle CAB=40^\circ\) and \(\angle DAB=80^\circ\)
\(\angle ADC=180^\circ-80^\circ=100^\circ\)
DB bisects angle D, so \(x=\frac{100^\circ}{2}=50^\circ\)