the measures of the angles of a triangle are in a ratio of 3:5:7.  what is the degree measure of the largest angle

In a triangle, the sum of the interior angles is always 180°. 

Let the measures of the angles be represented as \(3x\), \(5x\), and \(7x\), where \(x\) is a constant multiplier.

To find \(x\), we set up the equation:
\[
3x + 5x + 7x = 180°
\]
\[
15x = 180°
\]
\[
x = \frac{180°}{15} = 12°
\]

Now, to find the largest angle, we multiply \(x\) by 7 (since the largest angle corresponds to the 7 in the ratio):
\[
7x = 7 \times 12° = 84°
\]

Thus, the largest angle is **84°**.

Would you like more details or have any further questions?

Here are five related questions:
1. How do you find the smallest angle in the triangle?
2. What are the other two angles of the triangle in this problem?
3. Can a triangle have angles in any ratio that don't add up to 180°?
4. How would this problem change if the triangle was not a Euclidean triangle?
5. Can you explain why the angles in any triangle always add up to 180°?

**Tip:** For any triangle problem, always remember the sum of its interior angles is 180°.

The measures of the angles of a triangle are in a ratio of 3:5:7. What is the degree measure of the largest angle?

Learn how to find the largest angle in a triangle when the angles are in a ratio of 3:5:7. This step-by-step solution uses the angle sum property of triangles to find the degree measure of the largest angle, suitable for Grades 6-8.

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