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Answer:
Each base angle of one triangle is 54°
Step-by-step explanation:
Since the angles meeting in the center are congruent and all form 360° then it means each angle will be 360°/5 = 72°(since we have 5 angles).
Since they are all isosceles triangles, it means two base angles are equal and can be gotten by:
(180 – 72)/2 = 54°.
Each base angle of one triangle is 54°
The measure of a base angle of one of the triangles is 54°.
Given that,
A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex.
A regular pentagon is shown. Lines are drawn from each point to a point in the center to form congruent isosceles triangles.
The lengths of all lines are congruent. The total number of degrees of all center angles is 360 degrees.
The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent,
We have to determine,
What is the measure of the base angle of one of the triangles?
According to the question,
The lengths of all lines are congruent. The total number of degrees of all center angles is 360 degrees.
The total number of degrees in the center is 360°. If all five vertex angles meeting at the center are congruent,
The angles meeting in the center are congruent and all form 360°.
then it means each angle will be,
[tex]=\dfrac{360}{5}\\\\= 72 \ degree[/tex]
There are 5 angles.
Therefore,
All isosceles triangles, it means two base angles are equal and can be,
[tex]=\dfrac{180-72}{2}\\\\=\dfrac{108}{2}\\\\=54[/tex]
Hence, Each base angle of one triangle is 54°
To know more about Geometry click the link given below.
https://brainly.com/question/24863115
