If CE||DB, what is the value of x:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 85°
Two facts settle it: the angles of a triangle add up to 180°, and when a line crosses two parallel lines the alternate angles are equal. Here BC crosses the parallel lines DB and CE, so \(x=\angle DBC\). The 75° arc at D spans the whole angle ADC, from DA to DC.
In triangle ABD:
\(\angle ADB=180^\circ-110^\circ-30^\circ=40^\circ\)
\(\angle BDC=\angle ADC-\angle ADB=75^\circ-40^\circ=35^\circ\)
In triangle BDC:
\(\angle DBC=180^\circ-35^\circ-60^\circ=85^\circ\)
\(x=\angle BCE=\angle DBC=85^\circ\) (alternate angles, CE \(\parallel\) DB)
