Given ΔMNO, find the measure of ∠LMN.

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.

38°
52°
76°
104°

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sqdancefan sqdancefan · Answer 1 · 2019-10-02T02:25:50+02:00

Answer:

104°

Step-by-step explanation:

If segments NO and NM are congruent, then angles NMO and NOM are congruent. So, their supplements, angles NML and NOP are congruent. That is ...

∠NML ≅ ∠NOP = 104°

∠NML = 104°

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erinna erinna · Answer 2 · 2019-12-18T06:30:15+01:00

Answer:

Option D.

Step-by-step explanation:

Given information: MN ≅ NO

Isosceles triangle property : If two sides of a triangle and congruent then the angles opposite those sides are congruent.

Using Isosceles triangle property we get

[tex]\angle NMO\cong \angle NOM[/tex]

Segment LM forming a straight angle with segment MO.

[tex]\angle LMN+\angle NMO=180[/tex]

[tex]\angle NMO=180-\angle LMN[/tex]

Segment OP forming a straight angle with segment MO.

[tex]\angle NOP+\angle NOM=180[/tex]

[tex]\angle NOM=180-\angle NOP[/tex]

Since [tex]\angle NMO\cong \angle NOM[/tex], so

[tex]180-\angle LMN\cong 180-\angle NOP[/tex]

[tex]\angle LMN\cong \angle NOP[/tex]

It is given that measure of angle NOP is 104 degree.

[tex]m\angle LMN=104^{\circ}[/tex]

Therefore, the correct option is D.