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Jamar is building a doghouse with the front of the roof shaped like an isosceles triangle. Angles in a triangle add to degrees, and the base angles of an isosceles triangle so an equation for the angles in the roof triangle could be: Solve for x: x =

Jamar is building a doghouse with the front of the roof shaped like an isosceles triangle. Angles in a triangle add to degrees, and the base angles of an isosceles triangle so an equation for the angles in the roof triangle could be: Solve for x: x =

Elementary Geometry For College Students, 7e
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
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Question
**Building a Doghouse: A Geometry Exercise** Jamar is building a doghouse with the front structure as shown in the image. **Diagram Explanation:** The front of the doghouse is a brick structure with a triangular roof. Below are detailed observations and measurements from the diagram: 1. **Triangular Roof:** - One of the angles of the triangular roof is given as 50 degrees. - Another angle at the base of the triangle, opposite to the 50-degree angle, is marked as "x". **Understanding Triangle Angles:** - Angles in a triangle add up to 180 degrees. To find the unknown angle "x", we use the equation: \( x + 50^\circ + 90^\circ = 180^\circ\) \( x = 180^\circ - 50^\circ - 90^\circ \) \( x = 40^\circ\) In conclusion, the unknown angle "x" is 40 degrees. This type of exercise helps in understanding the basic properties of triangles and their internal angles. --- This transcription provides students and educators with a clear and detailed explanation to integrate an image into learning about geometry, specifically the sum of angles in a triangle.
Transcribed Image Text:**Building a Doghouse: A Geometry Exercise** Jamar is building a doghouse with the front structure as shown in the image. **Diagram Explanation:** The front of the doghouse is a brick structure with a triangular roof. Below are detailed observations and measurements from the diagram: 1. **Triangular Roof:** - One of the angles of the triangular roof is given as 50 degrees. - Another angle at the base of the triangle, opposite to the 50-degree angle, is marked as "x". **Understanding Triangle Angles:** - Angles in a triangle add up to 180 degrees. To find the unknown angle "x", we use the equation: \( x + 50^\circ + 90^\circ = 180^\circ\) \( x = 180^\circ - 50^\circ - 90^\circ \) \( x = 40^\circ\) In conclusion, the unknown angle "x" is 40 degrees. This type of exercise helps in understanding the basic properties of triangles and their internal angles. --- This transcription provides students and educators with a clear and detailed explanation to integrate an image into learning about geometry, specifically the sum of angles in a triangle.
### Constructing a Doghouse with an Isosceles Triangle Roof Jamar is building a doghouse with the front of the roof shaped like an isosceles triangle. ![Doghouse Diagram](image.png) **Concept Explanation:** - **Angles in a Triangle:** All angles in any triangle add up to 180 degrees. - **Isosceles Triangle:** An isosceles triangle has two sides of equal length, and thus, two angles of equal measure. **Problem:** - Given that the angles in a triangle add to 180 degrees and the base angles of an isosceles triangle are equal, set up an equation and solve for \( x \) which represents one of the base angles. **Steps to Solve:** 1. **Identify the Angles:** Label the base angles as \( x \). 2. **Equation Setup:** Since the sum of all angles in the triangle is 180 degrees, the equation will be: \[ x + x + \text{vertex angle} = 180 \text{ degrees} \] Substitute the known values and solve for \( x \). **Interactive Components:** - Fill in the blank for the total degrees in a triangle. - Provide the formula for the base angles of an isosceles triangle. - Enter the value of \( x \) after solving the equation. **Solution Placeholder:** - Angles in a triangle add to \( \boxed{180} \) degrees, and the base angles of an isosceles triangle are \( \boxed{x} \), so an equation for the angles in the roof triangle could be: \[ 2x + \text{vertex angle} = 180 \text{ degrees} \] - Solve for \( x \): \[ x = \boxed{\ } \] ### Practice Problems: 1. **Problem 1:** Solve for the base angles if the vertex angle is 40 degrees. 2. **Problem 2:** Given one base angle, find the other angles in the triangle.
Transcribed Image Text:### Constructing a Doghouse with an Isosceles Triangle Roof Jamar is building a doghouse with the front of the roof shaped like an isosceles triangle. ![Doghouse Diagram](image.png) **Concept Explanation:** - **Angles in a Triangle:** All angles in any triangle add up to 180 degrees. - **Isosceles Triangle:** An isosceles triangle has two sides of equal length, and thus, two angles of equal measure. **Problem:** - Given that the angles in a triangle add to 180 degrees and the base angles of an isosceles triangle are equal, set up an equation and solve for \( x \) which represents one of the base angles. **Steps to Solve:** 1. **Identify the Angles:** Label the base angles as \( x \). 2. **Equation Setup:** Since the sum of all angles in the triangle is 180 degrees, the equation will be: \[ x + x + \text{vertex angle} = 180 \text{ degrees} \] Substitute the known values and solve for \( x \). **Interactive Components:** - Fill in the blank for the total degrees in a triangle. - Provide the formula for the base angles of an isosceles triangle. - Enter the value of \( x \) after solving the equation. **Solution Placeholder:** - Angles in a triangle add to \( \boxed{180} \) degrees, and the base angles of an isosceles triangle are \( \boxed{x} \), so an equation for the angles in the roof triangle could be: \[ 2x + \text{vertex angle} = 180 \text{ degrees} \] - Solve for \( x \): \[ x = \boxed{\ } \] ### Practice Problems: 1. **Problem 1:** Solve for the base angles if the vertex angle is 40 degrees. 2. **Problem 2:** Given one base angle, find the other angles in the triangle.
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