Answer:
Therefore,
[tex]m\angle NQL=80\°[/tex]
By same-side interior angle theorem ,angle NQL and angle QLM are supplementary.
Step-by-step explanation:
Given:
LMNQ is a Parallelogram
∠QLM = 100°
To Find:
∠NQL = ?
Solution:
Same - Side - Interior Angle Theorem
:
The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line,
Then the same-side interior angles that are formed are supplementary, or add up to 180 degrees.
LMNQ is a Parallelogram ...........Given:
∴ LM || QN ..............Opposite Sides of Parallelogram are Parallel
By same-side interior angle theorem ,angle NQL and angle QLM are supplementary.
∴ [tex]\angle NQL+\angle QLM =180[/tex]
Substituting ∠QLM = 100° we get
[tex]\angle NQL+100 =180\\\angle NQL=180-100=80[/tex]
Therefore,
[tex]m\angle NQL=80\°[/tex]
