In ΔLMN, \overline{LN} LN
is extended through point N to point O, \text{m}\angle MNO = (5x-13)^{\circ}m∠MNO=(5x−13)
∘
, \text{m}\angle NLM = (x-4)^{\circ}m∠NLM=(x−4)
∘
, and \text{m}\angle LMN = (2x+19)^{\circ}m∠LMN=(2x+19)
∘
. Find \text{m}\angle NLM. m∠NLM

Step-by-step explanation:

Given a ΔLMN.

Line LN is extended to point O.

such that:

and

To find:

Solution:

Kindly refer to the attached image for the given triangle and dimensions of angles.

Let us recall the external angle property of a triangle:

The external angle of a triangle is equal to the sum of two opposite internal angles.

i.e.

Putting the value of in .

-2

7 - 9 = -2

reversed:

-2 + 9 = 7