Question

Please solve with explain

By the _____, angle NQL and _____, are _______.

Answer 1

The original question is incomplete, but it is likely asking about the angle between two vectors or a vector and a plane. This appears to involve the use of trigonometry, specifically the calculation of angles using the inverse cosine of the dot product of vectors. In physical applications, this is often used in force decomposition, yet without the full context or the associated figures, providing a definitive answer is not possible.

Step-by-step explanation:

The student's question is incomplete, making it challenging to provide an accurate solution without the full context or the figure referenced (angle NQL). However, the answer seems to pertain to understanding the angle between vectors, lines, or planes, which is a concept in trigonometry and can also relate to physics problems involving forces. In such calculations, vectors are typically used to represent physical quantities, and the angle between them is calculated using the dot product formula:

Angle between vectors A and B is obtained by taking the inverse cosine of the expression in Equation 2.34, which can be represented as:

A · B = Ax Bx + Ay By + Az Bz

AB

where A and B are vectors with components Ax, Ay, Az, and Bx, By, Bz respectively. If this question pertains to the angle between a force vector and an inclined plane, trigonometry is indeed used to decompose the force into components parallel and perpendicular to the plane, using the incline angle.

Answer 2

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\°`