Question

Select all the true statements. protractor with ray lq at 0 or 180, ray lp at 50 or 130, ray ol at 90, ray ln at 60 or 120 and ray lm at 0 or 180. Group of answer choices LaTeX: m\angle QLP\:+\:m\angle PLO=m\angle MLN+m\angle NLO m ∠ Q L P + m ∠ P L O = m ∠ M L N + m ∠ N L O m ∠ Q L P + m ∠ P L O = m ∠ M L N + m ∠ N L O m ∠ Q L P + m ∠ P L O = m ∠ M L N + m ∠ N L O LaTeX: m\angle NLO+m\angle OLP\:=\:m\angle NLP m ∠ N L O + m ∠ O L P = m ∠ N L P m ∠ N L O + m ∠ O L P = m ∠ N L P m ∠ N L O + m ∠ O L P = m ∠ N L P LaTeX: m\angle QLO-m\angle QLP\:=\:m\angle MLO-m\angle MLN m ∠ Q L O − m ∠ Q L P = m ∠ M L O − m ∠ M L N m ∠ Q L O − m ∠ Q L P = m ∠ M L O − m ∠ M L N m ∠ Q L O − m ∠ Q L P = m ∠ M L O − m ∠ M L N LaTeX: m\angle\:MLN\:=\:120 m ∠ M L N = 120 m ∠ M L N = 120 m ∠ M L N = 120 LaTeX: m\angle QLP\:=50

Answer 1

Given: Angle L N O ≅ Angle L N M

Angle O L N ≅ Angle M L N

Prove: Angle L N O ≅ Angle L N M

Triangles L O N and L M N share common side L N. Angles O L N and N L M are congruent. Angles O N L and L N M are congruent.

It is given that angle LNO is congruent to angle

✔ LNM

and angle OLN is congruent to angle

✔ MLN

. We know that side LN is congruent to side LN because of the

✔ reflexive property

. Therefore, because of

✔ ASA

, we can state that triangle LNO is congruent to triangle LNM.

Explanation:

Answer 2

m ∠ M L N = 120

m < QLP =50

Explanation:

Ray lq at 0 or 180,

ray lp at 50 or 130,

ray ol at 90,

ray ln at 60 or 120

and ray lm at 0 or 180

Lets substitute the values of the angles to check the given options

1) ∠ Q L P + m ∠ P L O =m< MLN+m< NLO m

50 +40= 120+30

90 is not equal to 150

2) m < QLO- m < QLP =m < MLO-m< MLN m

90-50 = 90-120

40 is not equal to 30

3) m< MLN\:=\:120 From the figure based on observation this is correct.

4) m < QLP =50 From the figure based on observation this is also correct.