> Next question Given the following non-regular pentagon find the measure of the unknown angle. Z 135° 150° 65° (52-8)9 1389 The unknown angle is degrees. Enter an integer or decimal number [more..] Question Help: Message instructor Get a similar question You can retry this question below Submit Question 97°F Sunny ME Q Search
> Next question Given the following non-regular pentagon find the measure of the unknown angle. Z 135° 150° 65° (52-8)9 1389 The unknown angle is degrees. Enter an integer or decimal number [more..] Question Help: Message instructor Get a similar question You can retry this question below Submit Question 97°F Sunny ME Q Search
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter1: The Six Trigonometric Functions
Section1.2: The Rectangular Coordinate System
Problem 92PS: Draw an angle in standard position whose terminal side contains the point (2, –3). Find the...
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![### Finding the Measure of the Unknown Angle in a Non-regular Pentagon
**Problem Statement:**
Given the following non-regular pentagon, find the measure of the unknown angle.
The pentagon has the following angles labeled:
- \( 65^\circ \)
- \( 135^\circ \)
- \( 150^\circ \)
- \( 138^\circ \)
- \( (5z - 8)^\circ \)
**Pentagon Diagram:**
```
+-------------+
/ \
/ \
65°/ \ 135°
/ \
/ \
/ \
/ \
+---------------------------+
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
+---------------------------+
```
**Given equations:**
- Angle A = 65°
- Angle B = 135°
- Angle C = 150°
- Angle D = 138°
- Angle E = (5z - 8)°
**Objective:**
Find the value of:
- \( z \) = [Input box]
- The unknown angle \( (5z - 8)^\circ \) = [Input box]
**Formula for the sum of interior angles of a polygon:**
For a pentagon, the sum of the interior angles is \( (5 - 2) \times 180^\circ = 540^\circ \).
### Steps to Solve:
1. Set up the equation to find \( z \):
\[65 + 135 + 150 + 138 + (5z - 8) = 540\]
2. Combine like terms:
\[488 + 5z - 8 = 540\]
\[480 + 5z = 540\]
3. Solve for \( z \):
\[5z = 540 - 480\]
\[5z = 60\]
\[z = \frac{60}{5}\]
\[z = 12\]
4. Calculate the unknown angle with \( z \) value:
\[ (5z - 8) = 5(12) - 8 = 60 - 8 \]
\[ \text{Unknown angle} = 52^\circ \]
### Answer:
- \( z =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F667d2c44-c256-432e-9387-2fb9fa6afe7c%2F9a326d52-1078-4b8e-ad8e-0be2169b6b64%2Ftp24y48_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Measure of the Unknown Angle in a Non-regular Pentagon
**Problem Statement:**
Given the following non-regular pentagon, find the measure of the unknown angle.
The pentagon has the following angles labeled:
- \( 65^\circ \)
- \( 135^\circ \)
- \( 150^\circ \)
- \( 138^\circ \)
- \( (5z - 8)^\circ \)
**Pentagon Diagram:**
```
+-------------+
/ \
/ \
65°/ \ 135°
/ \
/ \
/ \
/ \
+---------------------------+
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
| |
+---------------------------+
```
**Given equations:**
- Angle A = 65°
- Angle B = 135°
- Angle C = 150°
- Angle D = 138°
- Angle E = (5z - 8)°
**Objective:**
Find the value of:
- \( z \) = [Input box]
- The unknown angle \( (5z - 8)^\circ \) = [Input box]
**Formula for the sum of interior angles of a polygon:**
For a pentagon, the sum of the interior angles is \( (5 - 2) \times 180^\circ = 540^\circ \).
### Steps to Solve:
1. Set up the equation to find \( z \):
\[65 + 135 + 150 + 138 + (5z - 8) = 540\]
2. Combine like terms:
\[488 + 5z - 8 = 540\]
\[480 + 5z = 540\]
3. Solve for \( z \):
\[5z = 540 - 480\]
\[5z = 60\]
\[z = \frac{60}{5}\]
\[z = 12\]
4. Calculate the unknown angle with \( z \) value:
\[ (5z - 8) = 5(12) - 8 = 60 - 8 \]
\[ \text{Unknown angle} = 52^\circ \]
### Answer:
- \( z =
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