Question

In the diagram, angle O L M O L M is twice as large as angle P O N P O N . What is the size of angle O L M O L M ?

Answer 1

Given:

Angle OLM is twice as large as angle PON

To find:

The size of angle OLM

Solution:

As we can see that

∠OKJ  = 124°

And as we know that

∠OKJ  + ∠OKL = 180°

Therefore

124° +  ∠OKL = 180°

∠OKL = 56°

Now

∠KOL = ∠PON

These both angles are vertically opposite angles

In addition,

 ∠OLM = ∠OKL + ∠KOL  

i.e

The Exterior angle of triangle = Total of opposite two interior angles

Given that

angle OLM is twice as large as angle PON

So,

 ∠OLM  = 2 ∠PON

∠OLM  = 2∠KOL

Therefore

2∠KOL  = ∠OKL + ∠KOL

∠KOL  = ∠OKL

∠KOL  = 56°

Therefore

∠OLM  = 2∠KOL  

= 2 × 56°

= 112°

Hence, the size of angle OLM is 112°

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