Question
Find the value ofx. The diagram is not to scale.
45°
120°/
a. 105 b. 135 c. 75 d. 60
45°
120°/
a. 105 b. 135 c. 75 d. 60
Answers
Answered by
GPT-4o mini
To find the value of \(x\) based on the given angles, we'll assume that we're dealing with angles in a triangle or that these angles are part of a geometric figure.
Since the diagram is not provided, we can look at the angles you've given: \(45^\circ\) and \(120^\circ\), and we need to find the value of \(x\).
1. **Sum of angles in a triangle**: If \(45^\circ\) and \(120^\circ\) are two angles of a triangle, we can find the third angle \(x\) by using the property that the sum of the angles in a triangle is \(180^\circ\):
\[
x + 45 + 120 = 180
\]
Simplifying this:
\[
x + 165 = 180
\]
\[
x = 180 - 165
\]
\[
x = 15^\circ
\]
Since \(15^\circ\) is not among the answer choices (a. 105, b. 135, c. 75, d. 60), it suggests that these angles may not be part of a triangle.
2. **Exterior angle theorem**: If the \(120^\circ\) angle is an exterior angle to a triangle formed by \(45^\circ\) and angle \(x\), we can use the Exterior Angle Theorem, which states that the exterior angle is equal to the sum of the two non-adjacent interior angles.
So, we set up the equation:
\[
120 = 45 + x
\]
Solving for \(x\):
\[
x = 120 - 45
\]
\[
x = 75^\circ
\]
Thus, the value of \(x\) is \(75^\circ\), which corresponds to the option **c. 75**.
Since the diagram is not provided, we can look at the angles you've given: \(45^\circ\) and \(120^\circ\), and we need to find the value of \(x\).
1. **Sum of angles in a triangle**: If \(45^\circ\) and \(120^\circ\) are two angles of a triangle, we can find the third angle \(x\) by using the property that the sum of the angles in a triangle is \(180^\circ\):
\[
x + 45 + 120 = 180
\]
Simplifying this:
\[
x + 165 = 180
\]
\[
x = 180 - 165
\]
\[
x = 15^\circ
\]
Since \(15^\circ\) is not among the answer choices (a. 105, b. 135, c. 75, d. 60), it suggests that these angles may not be part of a triangle.
2. **Exterior angle theorem**: If the \(120^\circ\) angle is an exterior angle to a triangle formed by \(45^\circ\) and angle \(x\), we can use the Exterior Angle Theorem, which states that the exterior angle is equal to the sum of the two non-adjacent interior angles.
So, we set up the equation:
\[
120 = 45 + x
\]
Solving for \(x\):
\[
x = 120 - 45
\]
\[
x = 75^\circ
\]
Thus, the value of \(x\) is \(75^\circ\), which corresponds to the option **c. 75**.