Solve for the measure of the missing angle. (3x + 12)° 90⁰ 70° (4x-10) (3x-2)° Missing Angle
Solve for the measure of the missing angle. (3x + 12)° 90⁰ 70° (4x-10) (3x-2)° Missing Angle
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Problem:**
Solve for the measure of the missing angle.
**Diagram Analysis:**
The given diagram is a four-sided polygon with the following angle measures:
- The bottom left angle is a right angle (90°).
- The bottom right angle is 70°.
- The top left angle is expressed as \((3x + 12)°\).
- The top right angle is expressed as \((4x - 10)°\).
- The angle adjacent to the bottom right angle on the right side is expressed as \((3x - 2)°\).
**Solution Outline:**
To find the measure of the missing angle, follow these steps:
1. Recognize that the sum of the angles in a quadrilateral is 360°.
2. Set up an equation that represents the sum of the given angles equaling 360°.
3. Solve for \(x\).
4. Substitute the value of \(x\) back into the expressions for the angles to find their measures.
5. Calculate the missing angle.
**Step-by-Step Solution:**
1. The sum of all angles in a quadrilateral is:
\[
90° + 70° + (3x + 12)° + (4x - 10)° = 360°
\]
2. Simplify and solve for \(x\):
\[
90 + 70 + 3x + 12 + 4x - 10 = 360
\]
\[
162 + 7x = 360
\]
\[
7x = 360 - 162
\]
\[
7x = 198
\]
\[
x = 28.29
\]
3. Substitute \(x = 28.29\) back into each angle expression:
\[
(3x + 12)° = 3(28.29) + 12 = 84.87 + 12 = 96.87°
\]
\[
(4x - 10)° = 4(28.29) - 10 = 113.16 - 10 = 103.16°
\]
Therefore, the measure of the missing angle will be the remaining angle required to make the sum of all angles 360 degrees.
4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe53cea77-c966-4d47-ae93-d2c22a57e8a1%2F6f3c6ad6-b702-44bc-9c21-12ae4eb4c70f%2Fzecmxsx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Solve for the measure of the missing angle.
**Diagram Analysis:**
The given diagram is a four-sided polygon with the following angle measures:
- The bottom left angle is a right angle (90°).
- The bottom right angle is 70°.
- The top left angle is expressed as \((3x + 12)°\).
- The top right angle is expressed as \((4x - 10)°\).
- The angle adjacent to the bottom right angle on the right side is expressed as \((3x - 2)°\).
**Solution Outline:**
To find the measure of the missing angle, follow these steps:
1. Recognize that the sum of the angles in a quadrilateral is 360°.
2. Set up an equation that represents the sum of the given angles equaling 360°.
3. Solve for \(x\).
4. Substitute the value of \(x\) back into the expressions for the angles to find their measures.
5. Calculate the missing angle.
**Step-by-Step Solution:**
1. The sum of all angles in a quadrilateral is:
\[
90° + 70° + (3x + 12)° + (4x - 10)° = 360°
\]
2. Simplify and solve for \(x\):
\[
90 + 70 + 3x + 12 + 4x - 10 = 360
\]
\[
162 + 7x = 360
\]
\[
7x = 360 - 162
\]
\[
7x = 198
\]
\[
x = 28.29
\]
3. Substitute \(x = 28.29\) back into each angle expression:
\[
(3x + 12)° = 3(28.29) + 12 = 84.87 + 12 = 96.87°
\]
\[
(4x - 10)° = 4(28.29) - 10 = 113.16 - 10 = 103.16°
\]
Therefore, the measure of the missing angle will be the remaining angle required to make the sum of all angles 360 degrees.
4.
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