ABCDABCDABCD is a trapezium with AD∥BC AD \parallel BC AD∥BC and AB=ADAB = AD AB=AD. 0∘<θ<180∘ 0^\circ < \theta < 180^\circ 0∘<θ<180∘ is an angle such that ∠BAC=θ \angle BAC = \theta∠BAC=θ, ∠CAD=3θ \angle CAD = 3 \theta ∠CAD=3θ and ∠ACD=5θ \angle ACD = 5 \theta ∠ACD=5θ. What is the measure (in degrees) of θ\thetaθ?
Details and assumptions
A trapezium has a pair of parallel sides.