GH, KL and MN are straight lines. Find ∠p\angle p.

Recognising angles and their sizes中文
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Worked solution

4

1. Find the angle vertically opposite to $\angle GOK$

∠HOL=∠GOK=54∘\angle HOL = \angle GOK = 54^\circ (vertically opposite angles)

2. Use angles on a straight line to find $\angle p$

Since M,O,NM, O, N are collinear, ∠MOL+∠LOH+∠HON=180∘\angle MOL + \angle LOH + \angle HON = 180^\circ.
90∘+54∘+p=180∘90^\circ + 54^\circ + p = 180^\circ
p=180∘−144∘=36∘p = 180^\circ - 144^\circ = 36^\circ

Answer

36∘36^\circ (option 2)

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