### Investigation into the Sum of Interior Angles in Triangles**Question:**Peyton stated that she thought the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn’t always exactly 180°. Why do you think this happened? What might you say to Peyton?**Answer:**The sum of the measures of interior angles in any triangle is indeed always 180°. If Peyton found that the sum of angles in some of her triangles did not equal 180°, this could be due to a few possible reasons:1. **Measurement Error:** Using a protractor to measure angles can result in slight inaccuracies. Even small errors of one or two degrees for each measured angle can lead to a total that isn’t exactly 180°. 2. **Tool Precision:** The precision of the protractor could be a factor. If the protractor is not marked accurately, the measurements taken will not be exact.3. **Drawing Accuracy:** If the triangles drawn aren’t perfect (e.g., lines aren’t exactly straight, points aren’t exactly at the intended locations), the angles measured may deviate from their true values.4. **User Technique:** Differences in the way the protractor is used, such as not aligning it exactly with the sides of the triangle or not reading the scale correctly, can cause measurement discrepancies.**What to Say to Peyton:**I would explain to Peyton that while the mathematical principle states that the sum of the interior angles in a triangle is always 180°, practical measurements can introduce some errors. These errors can come from measurement tools, drawing inaccuracies, or slight mistakes in reading the protractor. I would encourage her to try measuring again with a focus on precision or consider averaging multiple sets of measurements to reduce the impact of any single error.**Related Visual Explanation Tools:***The image displayed above includes an interactive toolbar from a word processor which allows for formatting and editing text. Peyton can use these tools to document her findings and observations systematically:*- **B (Bold), I (Italic), U (Underline):** To highlight important points, such as the statement and the mathematical principle.- **Paragraph Formatting Options:** For organizing her document into readable sections.- **Insert Table/Chart:** To record and compare her measurements and observations in a structured manner.- **Insert Equation:** To denote mathematical principles clearly.

We need to explain what the error is.

Peyton stated that she thought that the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn't always exactly 180°. Why do you think this happened? What might you say to Peyton? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial 10pt

Peyton stated that she thought that the sum of the measures of interior angles in a triangle was always 180° but when she measured the angles in 10 triangles using a protractor, the sum wasn't always exactly 180°. Why do you think this happened? What might you say to Peyton? For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BIUS Paragraph V Arial 10pt

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks