Question

Identify the quadrant and reference angle for 145
°
.

A.
Quadrant I

B.
Quadrant II

C.
Quadrant III

D.
Quadrant IV

E.
35
°

F.
45
°

G.
180
°

Answer 1

To identify the quadrant and reference angle for \( 145^\circ \):

1. **Determine the quadrant**:
- The angle \( 145^\circ \) is between \( 90^\circ \) and \( 180^\circ \), which places it in **Quadrant II**.

2. **Determine the reference angle**:
- The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For angles in Quadrant II, the reference angle can be found using:
\[
\text{Reference Angle} = 180^\circ - \text{given angle}
\]
- Therefore, for \( 145^\circ \):
\[
\text{Reference Angle} = 180^\circ - 145^\circ = 35^\circ
\]

Combining these findings:

- The angle \( 145^\circ \) is in **Quadrant II** (B).
- The reference angle is \( 35^\circ \) (E).

So, the final answers are:
- **Quadrant II** (B)
- **Reference angle** \( 35^\circ \) (E)