Mathematics: Ngland, ales, Non- K 8 (60 inutes) In the diagram, angle OLM is twice as large as angle PON. L J K 124° M uestion 1 uestion 2 uestion 3 0 uestion 4 uestion 5 Р N uestion 6 uestion 7 What is the size of angle OLM? uestion 8

835.66cm²Step-by-step explanation:...

Ngland, ales, Non- K 8 (60 inutes) In the diagram,

KingOfLaBron23

29.01.2022

Question

In the diagram, angle OLM is twice as large as angle PON. What is the size of angle OLM?

$\angle OLM =112^\circ$

Step-by-step explanation:

Let Angle PON =x

Therefore: Angle OLM =2x

$\angle JKO +\angle OKL =180^\circ\\124^\circ + \angle OKL =180^\circ\\\angle OKL =180^\circ-124^\circ\\\angle OKL =56^\circ$

$\angle PON =\angle KOL =x $ (Vertical Angles)$

$\angle OKL +\angle KOL=\angle OLM $(Opposite Interior Angles of Triangle KOL)$

$56+x=2x\\2x-x=56\\x=56^\circ$

Therefore:

$\angle OLM =2x=2*56=112^\circ$

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