Question

26)which is the measure of an angle in standard position that is coterminal with an angle of 82°? a. -278° b. 8° c. -188° d. 98°

Explanation:

Step1: Recall coterminal angle rule

Coterminal angles differ by integer multiples of $360^\circ$, so we use $\theta + 360^\circ k$ where $k$ is any integer.

Step2: Test each option for $\theta=82^\circ$

For option A: $82^\circ + 360^\circ k = -278^\circ$
Solve for $k$: $360^\circ k = -278^\circ - 82^\circ = -360^\circ$
$k = \frac{-360^\circ}{360^\circ} = -1$, which is an integer.
Verify other options:

• Option B: $82^\circ + 360^\circ k = 8^\circ$ → $360^\circ k = -74^\circ$ → $k=-\frac{74}{360}$, not integer.
• Option C: $82^\circ + 360^\circ k = -188^\circ$ → $360^\circ k = -270^\circ$ → $k=-\frac{270}{360}$, not integer.
• Option D: $82^\circ + 360^\circ k = 98^\circ$ → $360^\circ k = 16^\circ$ → $k=\frac{16}{360}$, not integer.

Answer:

A. -278°