### 8.03 Semester Test: Grade 8 Semester B Test - Par**Problem Statement:**$\angle 1$ and $\angle 2$ are a linear pair, and $\angle 2$ and $\angle 3$ are vertical angles. $m\angle 1 = (5y - 8)^\circ$ and $m\angle 2 = (12 + 6y)^\circ$.What is $m\angle 3$?- 16°- 72°- 108°- 132°**Explanation:**The given problem involves understanding the relationships between linear pairs and vertical angles to solve for the measure of $\angle 3$.1. Since $\angle 1$ and $\angle 2$ are a linear pair, their measures add up to 180°: \[ m\angle 1 + m\angle 2 = 180^\circ \] Substitute the given expressions: \[ (5y - 8) + (12 + 6y) = 180 \] Simplify and solve for $y$: \[ 5y - 8 + 12 + 6y = 180 \] \[ 11y + 4 = 180 \] \[ 11y = 176 \] \[ y = 16 \]2. Substitute $y = 16$ back into the expression for $m\angle 2$: \[ m\angle 2 = 12 + 6(16) \] \[ m\angle 2 = 12 + 96 \] \[ m\angle 2 = 108^\circ \] 3. Since $\angle 2$ and $\angle 3$ are vertical angles, they are equal: \[ m\angle 3 = m\angle 2 = 108^\circ \]Thus, the correct answer is:**108°****Answer Choices Interaction:**On the webpage, the answer choices are presented as selectable options:- $ \quad $ 16°- $ \quad $ 72°

Answered: Image /qna-images/answer/2699e0ef-546c-4ee9-a0f8-f0df274f2650.jpg

Answered: Zland 22 are a linear pair, and 22 and…

Zland 22 are a linear pair, and 22 and 23 are vertical angles. m21 = (5y – 8)° and m22 = (12 + 6y). What is mZ3? O 16° O 72° O 108°

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.

Question

### 8.03 Semester Test: Grade 8 Semester B Test - Par

**Problem Statement:**

$\angle 1$ and $\angle 2$ are a linear pair, and $\angle 2$ and $\angle 3$ are vertical angles. $m\angle 1 = (5y - 8)^\circ$ and $m\angle 2 = (12 + 6y)^\circ$.

What is $m\angle 3$?
- 16°
- 72°
- 108°
- 132°

**Explanation:**

The given problem involves understanding the relationships between linear pairs and vertical angles to solve for the measure of $\angle 3$.

1. Since $\angle 1$ and $\angle 2$ are a linear pair, their measures add up to 180°:
\[
m\angle 1 + m\angle 2 = 180^\circ
\]
Substitute the given expressions:
\[
(5y - 8) + (12 + 6y) = 180
\]
Simplify and solve for $y$:
\[
5y - 8 + 12 + 6y = 180
\]
\[
11y + 4 = 180
\]
\[
11y = 176
\]
\[
y = 16
\]

2. Substitute $y = 16$ back into the expression for $m\angle 2$:
\[
m\angle 2 = 12 + 6(16)
\]
\[
m\angle 2 = 12 + 96
\]
\[
m\angle 2 = 108^\circ
\]

3. Since $\angle 2$ and $\angle 3$ are vertical angles, they are equal:
\[
m\angle 3 = m\angle 2 = 108^\circ
\]

Thus, the correct answer is:

**108°**

**Answer Choices Interaction:**

On the webpage, the answer choices are presented as selectable options:

- $ \quad $ 16°
- $ \quad $ 72°

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