https://file.aiquickdraw.com/mathbot/file/1725572072736z21gjbsy.jpg

We need to find the measure of angle \( e \) in the given triangle. To solve this, let's follow these steps:

### Step 1: Label the angles
The triangle is split into two triangles, and we can label the angles and lines to use basic geometric principles.

### Step 2: Sum of angles in a triangle
The sum of angles in any triangle is always \( 180^\circ \). We will apply this fact to both triangles.

### Step 3: Work with the lower triangle
In the lower triangle, we are given:
- \( e \) (unknown angle)
- \( 115^\circ \) (given exterior angle)
- \( 30^\circ \) (known angle)

In this triangle, \( e + 30^\circ + 115^\circ = 180^\circ \).

Let’s solve for \( e \):

\[
e = 180^\circ - 30^\circ - 115^\circ
\]

\[
e = 35^\circ
\]

Thus, the measure of angle \( e \) is \( 35^\circ \).

Would you like further explanation or clarification? Here are five related questions:

1. How can the exterior angle theorem help solve problems involving angles?
2. What other methods can be used to find unknown angles in triangles?
3. How can the properties of supplementary angles be applied in triangle problems?
4. What is the relationship between interior and exterior angles in polygons?
5. Can you describe other geometric principles that help solve multi-triangle problems?

**Tip**: Always check the sum of angles in a triangle to ensure accuracy, especially when using multiple angles or triangles in a diagram.

Find the measure of angle e in a triangle with angles 34°, 115°, and 30° given.

Learn how to find the measure of angle e in a triangle with given angles 34°, 115°, and 30°. This problem involves using the angle sum property and the exterior angle theorem, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation