Answer :
Final answer:
To find angles coterminal with a 145-degree angle, add or subtract multiples of 360 degrees. The coterminal angles of 145 degrees are 505 degrees, -215 degrees, and 865 degrees.
Explanation:
Angles that are coterminal with a 145-degree angle have the same initial side (starting side) and terminal side (ending side) as the given angle, but differ by a multiple of 360 degrees. To determine which angles in the given options are coterminal with 145 degrees, we need to add or subtract multiples of 360 from 145.
145 + 360 = 505 degrees (coterminal angle)
145 - 360 = -215 degrees (coterminal angle)
145 + 2(360) = 865 degrees (coterminal angle)
Therefore, the angles coterminal with a 145-degree angle are 505 degrees, -215 degrees, and 865 degrees, which correspond to options f, b, and g respectively.
