Question
In the diagram, angle OLM is twice as large as angle PON. What is the size of angle OLM?
Answer:
[tex]\angle OLM =112^\circ[/tex]
Step-by-step explanation:
Let Angle PON =x
Therefore: Angle OLM =2x
[tex]\angle JKO +\angle OKL =180^\circ\\124^\circ + \angle OKL =180^\circ\\\angle OKL =180^\circ-124^\circ\\\angle OKL =56^\circ[/tex]
[tex]\angle PON =\angle KOL =x $ (Vertical Angles)[/tex]
[tex]\angle OKL +\angle KOL=\angle OLM $(Opposite Interior Angles of Triangle KOL)[/tex]
[tex]56+x=2x\\2x-x=56\\x=56^\circ[/tex]
Therefore:
[tex]\angle OLM =2x=2*56=112^\circ[/tex]
