Each face of a pyramid is an isosceles triangle with a 70degrees vertex angle. What are the measures of the base​ angles?

In an isosceles triangle, the two base angles are equal, and the sum of all angles in any triangle must equal 180°.

Given:
- The vertex angle of the isosceles triangle is 70°.

To find the base angles, we can use the following equation:

\[
\text{Sum of all angles} = \text{Vertex angle} + 2 \times \text{Base angle}
\]
\[
180° = 70° + 2 \times \text{Base angle}
\]

Now, solve for the base angle:

\[
180° - 70° = 2 \times \text{Base angle}
\]
\[
110° = 2 \times \text{Base angle}
\]
\[
\text{Base angle} = \frac{110°}{2} = 55°
\]

Thus, the base angles are each 55°.

Would you like further details or have any questions?

Here are some related questions:
1. What is the total surface area of a pyramid with isosceles triangle faces?
2. How would the base angles change if the vertex angle was larger or smaller?
3. Can you calculate the height of the triangular face if given the side lengths?
4. What are the internal angles of a regular pyramid's base if it has more than 3 sides?
5. How do you calculate the volume of a pyramid using its height and base area?

**Tip**: In any polygon or triangle, always remember the sum of interior angles for quick checks and calculations!

Each face of a pyramid is an isosceles triangle with a 70-degree vertex angle. What are the measures of the base angles?

Learn how to calculate the base angles of an isosceles triangle with a 70° vertex angle. This step-by-step guide covers key geometric concepts, including the angle sum property and isosceles triangle properties. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation