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In the diagram to the right three lines intersect at n.The measure of < GNF is 60, and the measure of < MNL is 47. What is the measure of < HNK?

In the diagram to the right three lines intersect at nThe measure of lt GNF is 60 and the measure of lt MNL is 47 What is the measure of lt HNK class=

Respuesta :

texaschic101
< GNL = 60
< MNL = 47

< MNL and < GNH are vertical angles and are equal
so < GNH = 47

< GNL + < GNH + < HNK = 180....these angles form a straight line...so when added, they equal 180

60 + 47 + < HNK = 180
107 + < HNK = 180
< HNK = 180 - 107
< HNK = 73 <====

Measure of ∠HNK is equals to 73°.

What are linear pair angles?

" Linear angles are formed when the sum of pairs of adjacent angles is equals to 180°."

According to the question,

Measure of ∠GNF = 60°

Measure of ∠MNL = 47°

As per the linear pair angles definition ,

∠GNF, ∠FNM,  ∠MNL forms linear pair angles .

Therefore,

∠GNF + ∠FNM + ∠MNL = 180°

Substitute the given values we get,

60° + ∠FNM + 47° = 180°

⇒ ∠FNM = 180° - 107

               = 73°

As given three lines intersect at 'N'

∠FNM and ∠HNK are vertically opposite angles and are congruent.

Therefore,

Measure of ∠HNK = 73°

Hence, measure of ∠HNK is equals to 73°.

Learn more about linear pair angles here

https://brainly.com/question/26555759

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