Question
M7|L5 Using Equations to Solve for Unknown AnglesSign out
Line a and line b are intersecting lines. Use angle relationships shown in the diagram to find the value of n.
Solve on paper. Then, enter your answer on Zearn.
b
a
32ºnºnº
n =
Line a and line b are intersecting lines. Use angle relationships shown in the diagram to find the value of n.
Solve on paper. Then, enter your answer on Zearn.
b
a
32ºnºnº
n =
Answers
Answered by
GPT-4o mini
To find the value of \( n \) in the diagram with intersecting lines, we need to utilize the properties of angles formed by intersecting lines.
When two lines intersect, they create pairs of vertical angles that are equal and pairs of adjacent angles that are supplementary (their sum is \( 180^\circ \)).
Let's analyze the problem step-by-step:
1. **Identify the angles**: There are given angles, including \( 32^\circ \) and \( n^\circ \).
2. **Set up the equation using angle relationships**: If \( 32^\circ \) is adjacent to angle \( n \), we can use the supplementary angle relationship:
\[
32^\circ + n^\circ = 180^\circ
\]
3. **Solve for \( n \)**:
\[
n^\circ = 180^\circ - 32^\circ
\]
\[
n^\circ = 148^\circ
\]
Thus, the value of \( n \) is \( 148 \).
So, you should enter:
\[
n = 148
\]
When two lines intersect, they create pairs of vertical angles that are equal and pairs of adjacent angles that are supplementary (their sum is \( 180^\circ \)).
Let's analyze the problem step-by-step:
1. **Identify the angles**: There are given angles, including \( 32^\circ \) and \( n^\circ \).
2. **Set up the equation using angle relationships**: If \( 32^\circ \) is adjacent to angle \( n \), we can use the supplementary angle relationship:
\[
32^\circ + n^\circ = 180^\circ
\]
3. **Solve for \( n \)**:
\[
n^\circ = 180^\circ - 32^\circ
\]
\[
n^\circ = 148^\circ
\]
Thus, the value of \( n \) is \( 148 \).
So, you should enter:
\[
n = 148
\]