Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 17, 2023

Find the quadrant of the angle $177^{\circ}$ .

STEP 1

Assumptions
1. The angle is measured in degrees.
2. The angle measurement is positive.
3. The angle measurement starts from the positive x-axis and moves in a counterclockwise direction.
4. A full circle is $360^{\circ}$ .
5. Each quadrant of the coordinate plane spans $90^{\circ}$ .

STEP 2

Identify the range of degrees that each quadrant covers.
1. Quadrant I: $0^{\circ}$ to $90^{\circ}$ .
2. Quadrant II: $90^{\circ}$ to $180^{\circ}$ .
3. Quadrant III: $180^{\circ}$ to $270^{\circ}$ .
4. Quadrant IV: $270^{\circ}$ to $360^{\circ}$ .

STEP 3

Determine which range the given angle, $177^{\circ}$ , falls into.
Since $177^{\circ}$ is greater than $90^{\circ}$ but less than $180^{\circ}$ , it falls into the range of Quadrant II.

STEP 4

Name the quadrant in which the angle lies.
The angle $177^{\circ}$ lies in Quadrant II.

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