Given the B-sided figure below with exterior angle measures as shown, what is the value of X? 75° 68% A B C D 15 x=148 x=125" x=55* x= 105⁰ 32⁰ 28% 201
Given the B-sided figure below with exterior angle measures as shown, what is the value of X? 75° 68% A B C D 15 x=148 x=125" x=55* x= 105⁰ 32⁰ 28% 201
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
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Transcribed Image Text:**Problem Statement:**
Given the 8-sided figure below with exterior angle measures as shown, what is the value of \( x \)?
**Diagram:**
In the diagram, an 8-sided irregular polygon is presented with the following exterior angles labeled (clockwise from the top as seen in the provided figure):
- \( 68^\circ \)
- \( 75^\circ \)
- \( x \)
- \( 67^\circ \)
- \( 20^\circ \)
- \( 28^\circ \)
- \( 32^\circ \)
- \( 15^\circ \)
**Answer Choices:**
A) \( x = 148^\circ \)
B) \( x = 125^\circ \)
C) \( x = 55^\circ \)
D) \( x = 105^\circ \)
**Solution:**
To determine the value of \( x \), recall that the sum of all exterior angles of any polygon is always \( 360^\circ \).
Sum of given exterior angles + \( x \) = \( 360^\circ \)
So,
\( 68 + 75 + x + 67 + 20 + 28 + 32 + 15 = 360 \)
Calculating the sum of the known exterior angles:
\( 68 + 75 + 67 + 20 + 28 + 32 + 15 = 305 \)
Now, solve for \( x \):
\( 305 + x = 360 \)
\( x = 360 - 305 \)
\( x = 55 \)
**Correct Answer:**
C) \( x = 55^\circ \)
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