Question

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

Answer 1

112

Explanation:

Answer 2

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`

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`