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In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54\(^{\circ}\) ...


Question

In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54\(^{\circ}\) and angle MKN is 35\(^{\circ}\), calculate the size of angle KMN.

Options

A) 91\(^{\circ}\)

B) 89\(^{\circ}\)

C) 37\(^{\circ}\)

D) 19\(^{\circ}\)

The correct answer is C.

Explanation:

In the diagram above, \(\alpha\) = 54\(^{\circ}\)(alternate angles; KL||MN) < KNM = 2\(\alpha\) (LN is bisector of < KNM) = 108\(^{\circ}\)

35\(^{\circ}\) + < KMN + 108\(^{\circ}\) = 180\(^{\circ}\)(sum of angles of \(\bigtriangleup\))

< KMN + 143\(^{\circ}\) = 180\(^{\circ}\)

< KMN = 180\(^{\circ}\) - 143\(^{\circ}\)

= 37\(^{\circ}\)


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Discussion (2)

  • In the diagram above, \(\alpha\) = 54\(^{\circ}\)(alternate angles; KL||MN) < KNM = 2\(\alpha\) (LN is bisector of < KNM) = 108\(^{\circ}\)

    35\(^{\circ}\) + < KMN + 108\(^{\circ}\) = 180\(^{\circ}\)(sum of angles of \(\bigtriangleup\))

    < KMN + 143\(^{\circ}\) = 180\(^{\circ}\)

    < KMN = 180\(^{\circ}\) - 143\(^{\circ}\)

    = 37\(^{\circ}\)

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