**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 RoofJamar 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.

Isosceles triangle: The base angles are equal i.e, The sides opposite to the base angle are…

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

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.

### 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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