Question
Solve for
\[x\] in the diagram below.
Two lines intersect forming angles. One of the angles is marked and labeled as 60 degrees. Another angle opposite to this is marked and labeled as parenthesis open x plus 45 parenthesis closed degrees. The angle between these two is divided by a ray into two parts.
\[x\] in the diagram below.
Two lines intersect forming angles. One of the angles is marked and labeled as 60 degrees. Another angle opposite to this is marked and labeled as parenthesis open x plus 45 parenthesis closed degrees. The angle between these two is divided by a ray into two parts.
Answers
GPT-4o mini
To solve for \( x \), we need to use the fact that vertically opposite angles are equal and the relationship between the angles formed by intersecting lines.
From the description you provided, we can summarize the information as follows:
1. There is an angle of \( 60^\circ \).
2. The angle opposite to this (which is vertically opposite) is given as \( x + 45^\circ \).
Since vertically opposite angles are equal, we can set up the following equation:
\[
x + 45^\circ = 60^\circ
\]
Next, we will solve for \( x \):
1. Subtract \( 45^\circ \) from both sides:
\[
x = 60^\circ - 45^\circ
\]
2. This simplifies to:
\[
x = 15^\circ
\]
Thus, the solution for \( x \) is:
\[
\boxed{15}
\]
From the description you provided, we can summarize the information as follows:
1. There is an angle of \( 60^\circ \).
2. The angle opposite to this (which is vertically opposite) is given as \( x + 45^\circ \).
Since vertically opposite angles are equal, we can set up the following equation:
\[
x + 45^\circ = 60^\circ
\]
Next, we will solve for \( x \):
1. Subtract \( 45^\circ \) from both sides:
\[
x = 60^\circ - 45^\circ
\]
2. This simplifies to:
\[
x = 15^\circ
\]
Thus, the solution for \( x \) is:
\[
\boxed{15}
\]