Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter10: Measurement, Area, And Volume
Section10.1: Triangles
Problem 1C
Related questions
Question
PLS HELPP
![This image depicts a triangle problem commonly found in geometry sections of mathematics education.
**Triangle Problem Description:**
- The triangle is drawn with one of its sides extended, forming an exterior angle.
- The interior angles are marked as follows:
- The top angle is labeled as \(x^\circ\).
- The bottom-left angle is given as \(80^\circ\).
- The exterior angle formed outside the triangle is labeled as \(145^\circ\).
**Objective:**
- The problem asks to find the value of \(x^\circ\).
**Explanation:**
The exterior angle theorem in geometry states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, to find \(x^\circ\), use the formula:
\[ x^\circ + 80^\circ = 145^\circ \]
Solving for \(x^\circ\), we get:
\[ x^\circ = 145^\circ - 80^\circ = 65^\circ \]
Thus, the value of \(x^\circ\) is \(65^\circ\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d706a7d-bed2-424b-a0a5-50f9026558ee%2F8b62952f-8e95-4563-a826-ef5d775e0047%2Fkzjytu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:This image depicts a triangle problem commonly found in geometry sections of mathematics education.
**Triangle Problem Description:**
- The triangle is drawn with one of its sides extended, forming an exterior angle.
- The interior angles are marked as follows:
- The top angle is labeled as \(x^\circ\).
- The bottom-left angle is given as \(80^\circ\).
- The exterior angle formed outside the triangle is labeled as \(145^\circ\).
**Objective:**
- The problem asks to find the value of \(x^\circ\).
**Explanation:**
The exterior angle theorem in geometry states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, to find \(x^\circ\), use the formula:
\[ x^\circ + 80^\circ = 145^\circ \]
Solving for \(x^\circ\), we get:
\[ x^\circ = 145^\circ - 80^\circ = 65^\circ \]
Thus, the value of \(x^\circ\) is \(65^\circ\).
Expert Solution

Step 1: External angle theorem of a triangle
According to External Angle theorem of a triangle , An ecterior angle of a triangle is equals to
the sum of two interior angles
Given Interior angles are
Given Exterior angle is
Step by step
Solved in 3 steps with 4 images

Recommended textbooks for you

Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage

Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage