Question

Find the m∠NMO. Show your work in the scratchpad.

Answer 1

An isosceles triangle is one which has two equal sides and angles. Therefore, the measure of <NMO required in the given question is $20^{o}$.

An isosceles triangle is a type of triangle which has two equal sides, thus angles.

So that comparing the triangles in the given question, we have:

i. ΔNMQ, ΔMPQ, ΔOPM, and ΔNMO are all isosceles triangles.

Thus;

<MQN = <MNQ = $60^{o}$ (isosceles triangle base angle property)

So that;

<QMN = $180^{o}$ - (<MQN + <MNQ)

           = $180^{o}$ - $120^{o}$

<QMN = $60^{o}$

ii. In triangle MOP, we have;

<MPO = <MOP = $80^{o}$ (base angle property of isosceles triangle)

Then,

<PMO = $180^{o}$ - ($80^{o}$ +

        = $180^{o}$ - $160^{o}$)

<PMO = $20^{o}$

But,

<QMP + <NMO = ($60^{o}$ - $20^{o}$)

                         = $40^{o}$

Since <QMP = <NMO, then;

m<NMO = $\frac{40^{o} }{2}$

              = $20^{o}$

Thus, the measure of <NMO is $20^{o}$.

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