Question

find the measure of an angle between (0^{circ}) and (360^{circ}) coterminal with an angle of (-157^{circ}) in standard position.
(67^{circ})
(157^{circ})
(23^{circ})
(203^{circ})

find the measure of an angle between (0^{circ}) and (360^{circ}) coterminal with an angle of (-278^{circ}) in standard position.
(98^{circ})
(82^{circ})
(188^{circ})
(278^{circ})

Explanation:

First problem:

Step1: Recall coterminal angle formula

Coterminal angles are given by \(\theta + 360n\), where \(n\in\mathbb{Z}\). For \(\theta=- 157^{\circ}\), we want \(0^{\circ}\leq\theta + 360n\leq360^{\circ}\). Let \(n = 1\), then \(-157^{\circ}+360^{\circ}\).

$$ -157^{\circ}+360^{\circ}=203^{\circ} $$

Second problem:

Step1: Use coterminal angle formula

For \(\theta=-278^{\circ}\), use \(\theta + 360n\). Let \(n = 1\), then \(-278^{\circ}+360^{\circ}\).

$$ -278^{\circ}+360^{\circ}=82^{\circ} $$

Answer:

First problem: \(203^{\circ}\) (the fourth option). Second problem: \(82^{\circ}\) (the second option).