A star patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale I NEED HELP ANYONE?

Applying the theorem of the exterior angle of a triangle, the value of x in the image given is:

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:

Therefore:

Therefore, applying the theorem of the exterior angle of a triangle, the value of x in the image given is:

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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°

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