https://r2.erweima.ai/mathbot/image/1726398493195b5q992bt.jpg

We are given a triangle \( GHI \) with the measures of its angles:

- \( m \angle G = (x - 5)^\circ \)
- \( m \angle H = (x - 5)^\circ \)
- \( m \angle I = (4x + 4)^\circ \)

Since the sum of the angles in any triangle is always \( 180^\circ \), we can set up the following equation:

\[
(x - 5) + (x - 5) + (4x + 4) = 180
\]

Let's solve this equation step by step.

### Step 1: Combine like terms:
\[
x - 5 + x - 5 + 4x + 4 = 180
\]
\[
6x - 6 = 180
\]

### Step 2: Add 6 to both sides:
\[
6x = 186
\]

### Step 3: Divide by 6:
\[
x = 31
\]

Now that we have the value of \( x \), we can find the measures of the angles.

### Step 4: Calculate the angles:
- \( m \angle G = m \angle H = x - 5 = 31 - 5 = 26^\circ \)
- \( m \angle I = 4x + 4 = 4(31) + 4 = 124 + 4 = 128^\circ \)

Thus, the degree measures of the angles are:
- \( m \angle G = 26^\circ \)
- \( m \angle H = 26^\circ \)
- \( m \angle I = 128^\circ \)

Would you like further explanation on any part of this solution? Here are some follow-up questions you might consider:

1. Why do the angles in a triangle always add up to \( 180^\circ \)?
2. How would this process change if the triangle were not a regular triangle?
3. Could this triangle be classified as isosceles? Why or why not?
4. What would happen if \( m \angle I \) had a different expression, say \( (5x + 4)^\circ \)?
5. Can you use the Law of Sines or Law of Cosines with the given angles?

**Tip:** Always ensure the sum of the angles equals \( 180^\circ \) when dealing with triangles!

In the triangle below, suppose that m∠G = (x - 5)°, m∠H = (x - 5)°, and m∠I = (4x + 4)°. Find the degree measure of each angle in the triangle.

This problem involves using algebra and the Triangle Angle Sum Theorem to find the measures of the angles in a triangle. The angles are represented by the expressions (x - 5)° and (4x + 4)°. Follow the step-by-step process to solve for x and determine the degree measures of the angles. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation