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 .

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.