Question

Given ΔMNO, find the measure of ∠LMN.

Answer 1

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

$\angle NMO\cong \angle NOM$

Segment LM forming a straight angle with segment MO.

$\angle LMN+\angle NMO=180$

$\angle NMO=180-\angle LMN$

Segment OP forming a straight angle with segment MO.

$\angle NOP+\angle NOM=180$

$\angle NOM=180-\angle NOP$

Since $\angle NMO\cong \angle NOM$, so

$180-\angle LMN\cong 180-\angle NOP$

$\angle LMN\cong \angle NOP$

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

$m\angle LMN=104^{\circ}$

Therefore, the correct option is D.

Answer 2

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°