In the figure, if PQ∥RS, ∠MXQ=135∘ and ∠MYR=40∘, find ∠XMY. [4 MARKS]
Concept: 2 Marks
Application: 2 Marks
Through point M, draw a line AB parallel to the line PQ.
ABPQ and PQRS
∠QXM and ∠XMB are interior angles on the same side of the transversal XM.
∠QXM+∠XMB=180∘ (Sum of the interior angles on the same side of transversal XM is supplementary)
135∘+∠XMB=180∘
∠XMB=180∘−135∘=45∘
∠YMB=∠MYR=40∘ [alternate angles]
∠XMY=∠XMB+∠BMY
∠XMY=45∘+40∘=85∘