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Each face of a pyramid is an isosceles triangle with a 76 degree vertex angle. What are the measures of the base angles?

Respuesta :

gmoneyy
The sum of interior angles is 180°.
If you know that the vertex angle is 76° and the other two angles are equal, then subtract 76 from 180 which gives you 104. Then divide 104 by 2 to get the measure of your base angles.
MrRoyal

The measure of the base angles is 52 degrees

The vertex angle (v) is given as:

[tex]v = 76^o[/tex]

Represent the base angles with b.

The angles in a triangle add up to 180 degrees.

So, we have:

[tex]v + b + b = 180[/tex]

Add b and b

[tex]v + 2b = 180[/tex]

Substitute 76 for v

[tex]76 + 2b = 180[/tex]

Subtract 76 from both sides

[tex]76 - 76 + 2b = 180 - 76[/tex]

[tex]2b = 180 - 76[/tex]

[tex]2b = 104[/tex]

Divide both sides by 2

[tex]b = 52[/tex]

Hence, the measure of the base angles is 52 degrees

Read more about isosceles triangles at:

https://brainly.com/question/11884412

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