https://file.aiquickdraw.com/mathbot/file/1728590919299e8xx49bx.jpg

In the image, we see an isosceles triangle where two sides are marked as equal, and one angle is given as \(46^\circ\). We are tasked with finding the unknown variable \(n\), which likely represents the measure of one of the two equal angles.

### Solution:

For an isosceles triangle, two angles are equal, and the sum of all the interior angles of any triangle is \(180^\circ\). 

Let the two equal angles (opposite the equal sides) be denoted by \(n\). Since the sum of the angles in the triangle must equal \(180^\circ\), we can set up the following equation:

\[
n + n + 46^\circ = 180^\circ
\]

Simplifying this:

\[
2n + 46^\circ = 180^\circ
\]

Subtracting \(46^\circ\) from both sides:

\[
2n = 134^\circ
\]

Now, dividing by 2:

\[
n = 67^\circ
\]

Thus, the value of \(n\) is \(67^\circ\).

Would you like any additional details or have questions about this solution?

Here are 5 follow-up questions for further understanding:
1. What are the properties of an isosceles triangle?
2. How do we calculate the sum of angles in any triangle?
3. Can this problem be solved using trigonometric functions?
4. What is the relationship between the base angles and vertex angle in an isosceles triangle?
5. What happens if one angle in an isosceles triangle is a right angle?

**Tip:** Always remember that the sum of interior angles in any triangle is \(180^\circ\), and this rule applies universally!

Find the value of n in an isosceles triangle with one angle given as 46° and two equal sides.

Learn how to find the unknown angle in an isosceles triangle where one angle is given as 46°. This problem uses key geometry concepts, including the sum of angles in a triangle and properties of isosceles triangles. 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