Answer/Step-by-step explanation:
We know that sin 60° = √3/2, and we can use this information to find cos 60°:
cos 60° = √(1 - sin^2 60°) = √(1 - 3/4) = √(1/4) = 1/2.
To find the measure of angle 3, we can use the formula:
cos(180° - 2x) = -cos(2x)
We want to solve for x when cos 2x = √(√3/2) = √3/2 * 1/√2 = √3/2√2
cos(180° - 2x) = -cos(2x)
cos(2x) = √3/2√2
180° - 2x = 150° or 210°
x = 15° or 35°
Therefore, the measure of angle 3 can be either 15° or 35°.