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A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex. The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent, what is the measure of a base angle of one of the triangles? 54° 72° 108° 144°

A regular pentagon is created using the bases of five congruent isosceles triangles joined at a common vertex The total number of degrees in the center is 360 I class=

Respuesta :

It's 54 degrees.

The internet is a wonderful friend. Type in "Pentagon split into triangles" on google images and you will find a diagram that finds it.
calculista

Answer:

[tex]54\°[/tex]

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides and two equal angles

The two equal angles are the base angles and the third angle is the vertex angle

In this problem

The vertex angle of one of the isosceles triangle is equal to

[tex]360\°/5=72\°[/tex]

The sum of the internal angles of the triangle is equal to [tex]180\°[/tex]

Let

x------> the measure of a base angle of one of the isosceles triangle

so

[tex]2x+72\°=180\°[/tex]

solve for x

[tex]2x=180\°-72\°[/tex]

[tex]2x=108\°[/tex]

[tex]x=54\°[/tex]

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