Question

Ngland,

Answer 1

Question

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

Answer:

$\angle OLM =112^\circ$

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:

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