The measure of the seven angles in a nonagon measure 138°, 154°, 145°, 132°, 128°, 147°, and 130°. If the two remaining angles are equal in measure, what is the measure of each angle?
The measure of the seven angles in a nonagon measure 138°, 154°, 145°, 132°, 128°, 147°, and 130°. If the two remaining angles are equal in measure, what is the measure of each angle?
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:**
The measure of the seven angles in a nonagon measure \(138^\circ\), \(154^\circ\), \(145^\circ\), \(132^\circ\), \(128^\circ\), \(147^\circ\), and \(130^\circ\). If the two remaining angles are equal in measure, what is the measure of each angle?
**Explanation:**
A nonagon is a nine-sided polygon, and the sum of the interior angles of a polygon can be determined using the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides. For a nonagon (\( n = 9 \)):
\[ \text{Sum of interior angles} = (9 - 2) \times 180^\circ = 7 \times 180^\circ = 1260^\circ \]
From the problem, the sum of the given seven angles is:
\[ 138^\circ + 154^\circ + 145^\circ + 132^\circ + 128^\circ + 147^\circ + 130^\circ = 974^\circ \]
Let the measure of each of the two remaining equal angles be \( x \). Then:
\[ 974^\circ + 2x = 1260^\circ \]
Solving for \( x \):
\[ 2x = 1260^\circ - 974^\circ \]
\[ 2x = 286^\circ \]
\[ x = \frac{286^\circ}{2} \]
\[ x = 143^\circ \]
Thus, the measure of each of the two remaining angles is \( 143^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53aa649d-9d5d-4ca8-bdc5-0ee81160dadc%2Fe64418fb-8f79-4c11-a6f7-6dac1cd41c5f%2Fxe5zgxi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
The measure of the seven angles in a nonagon measure \(138^\circ\), \(154^\circ\), \(145^\circ\), \(132^\circ\), \(128^\circ\), \(147^\circ\), and \(130^\circ\). If the two remaining angles are equal in measure, what is the measure of each angle?
**Explanation:**
A nonagon is a nine-sided polygon, and the sum of the interior angles of a polygon can be determined using the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides. For a nonagon (\( n = 9 \)):
\[ \text{Sum of interior angles} = (9 - 2) \times 180^\circ = 7 \times 180^\circ = 1260^\circ \]
From the problem, the sum of the given seven angles is:
\[ 138^\circ + 154^\circ + 145^\circ + 132^\circ + 128^\circ + 147^\circ + 130^\circ = 974^\circ \]
Let the measure of each of the two remaining equal angles be \( x \). Then:
\[ 974^\circ + 2x = 1260^\circ \]
Solving for \( x \):
\[ 2x = 1260^\circ - 974^\circ \]
\[ 2x = 286^\circ \]
\[ x = \frac{286^\circ}{2} \]
\[ x = 143^\circ \]
Thus, the measure of each of the two remaining angles is \( 143^\circ \).
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