In the diagram, angle
O
L
M
is twice as large as angle
P
O
N
.
What is the size of angle
O
L
M
?
Answers
Given : angle OLM is twice as large as angle PON
To find : size of angle OLM
Solution:
∠OKJ = 124°
∠OKJ + ∠OKL = 180°
=> 124° + ∠OKL = 180°
=> ∠OKL = 56°
∠KOL = ∠PON ( vertically opposite angle )
∠OLM = ∠OKL + ∠KOL ( Exterior angle of triangle = Sum of opposite two interior angles)
angle OLM is twice as large as angle PON
=> ∠OLM = 2 ∠PON
=> ∠OLM = 2∠KOL
2∠KOL = ∠OKL + ∠KOL
=> ∠KOL = ∠OKL
=> ∠KOL = 56°
∠OLM = 2∠KOL = 2 * 56° = 112°
∠OLM = 112°
size of angle OLM = 112°
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