Each face of a pyramid is an isosceles triangle wish a 62° vertex angle? What are the meeasures of the base angle?
59 is your answer since 180-62=118 and 118/2=59
since the three angles add up to 180, each base angle has measure x, where
2x+62 = 180
Now find x.
To find the measures of the base angles of the pyramid, we need to determine the measure of the congruent angles in the isosceles triangles.
Let's denote the base angle of each isosceles triangle as x. Since the vertex angle of the isosceles triangle is 62 degrees, we can use the property of the triangle that states the sum of all angles in a triangle is 180 degrees.
In the case of the isosceles triangle, we have two congruent angles (base angles) and a vertex angle. Therefore, we can write the equation:
x + x + 62 = 180
Combining like terms, we have:
2x + 62 = 180
Subtracting 62 from both sides:
2x = 180 - 62
Simplifying:
2x = 118
Dividing both sides by 2:
x = 118 / 2
x = 59
Therefore, the measure of each base angle of the isosceles triangle (and hence the pyramid) is 59 degrees.
To find the measures of the base angles of the pyramid, we need to consider the properties of isosceles triangles.
In an isosceles triangle, the base angles are equal. Let's call the measure of each base angle of the pyramid x. Since each face of the pyramid is an isosceles triangle with a 62° vertex angle, the vertex angle and each base angle form a triangle.
The sum of the angles in a triangle is always 180°. In this case, the 62° vertex angle, along with the two base angles (each x°) gives us the equation:
62° + x° + x° = 180°.
Combining like terms, we have:
62° + 2x° = 180°.
Subtracting 62° from both sides:
2x° = 118°.
Dividing both sides by 2:
x° = 59°.
Therefore, each base angle of the pyramid measures 59°.