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Given ΔMNO, find the measure of ∠MNO. Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent. 28° 38° 52° 76°

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akposevictor

Applying the properties of an isosceles triangle and the sum of a triangle, the measure of angle MNO is: a. [tex]28^{\circ}[/tex]

The figure showing ΔMNO is in the attachment below.

ΔMNO is an isosceles triangle because sides MN and NO are congruent.

Also, the angles opposite each of the congruent sides will be equal also. i.e. m<NOM = m<NMO.

  • Given:

m<NOP = 104 degrees

  • Thus:

m<MNO = [tex]180 - 2(180 - m\angle NOP)[/tex] (isosceles triangle)

  • Substitute

m<MNO = [tex]180 - 2(180 - 104)[/tex]

[tex]m<MNO = 180 - 2(76)\\\\m<MNO = 180 - 152\\\\m<MNO = 28^{\circ}[/tex]

Therefore, applying the properties of an isosceles triangle and the sum of a triangle, the measure of angle MNO is: a. [tex]28^{\circ}[/tex]

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