From the figure, find x.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 70
The lines AB and CD cross at O, so the vertically opposite angles at O are equal: \(\angle AOC=\angle DOB\). The angles of a triangle add up to \(180^\circ\), so \(\angle AOC\) can be found from triangle AOC and then used in triangle DOB.
In triangle AOC: \(\angle AOC=180^\circ-90^\circ-45^\circ=45^\circ\)
So \(\angle DOB=45^\circ\)
In triangle DOB: \(x=180^\circ-65^\circ-45^\circ=70^\circ\)