Question

Please solve with explain By the _____, angle NQL and _____, are _______.

Answer 1

Answer:

Therefore,

$m\angle NQL=80\°$

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.

∴ $\angle NQL+\angle QLM =180$

Substituting ∠QLM = 100° we get

$\angle NQL+100 =180\\\angle NQL=180-100=80$

Therefore,

$m\angle NQL=80\°$