Respuesta :

elcharly64

Answer:

x = 81°

Step-by-step explanation:

Angles in a triangle

The sum of internal angles of a triangle is 180°

Angle x is an internal angle of the triangle shown in the figure below, where another angle y has been added.

For the construction of the figure, y is the supplementary angle of 105°, thus:

y = 180° - 105° = 75°

The internal angles of the triangle must comply:

24° + 75° + x = 180°

Solving for x:

x = 180° - 24° - 75°

x = 81°

Ver imagen elcharly64
akposevictor

Applying the theorem of the exterior angle of a triangle, the value of x in the image given is: [tex]\mathbf{x = 81^{\circ}}[/tex]

Recall:

The exterior angle theorem of a triangle states that the sum of the two interior angles of a triangle are congruent to the exterior angle opposite to them.

Thus:

  • 24 and x are two interior angles of the triangle.
  • 105 degrees is the exterior angle.

Therefore:

[tex]24 + x = 105[/tex]

  • Solve for x

[tex]x = 105 - 24\\\mathbf{x = 81^{\circ}}[/tex]

Therefore, applying the theorem of the exterior angle of a triangle, the value of x in the image given is: [tex]\mathbf{x = 81^{\circ}}[/tex]

Learn more here:

https://brainly.com/question/4164600

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