Ineed what are the measures of angles a, b, and c? show your work and explain your answers.

two straight lines intersect at a point to form angle a. the measure of the angle opposite to angle a is 30 degrees. angle a is the angle of a right triangle having another angle equal to b. a triangle with one angle labeled c is on the left of the figure. the angle adjacent to c is labeled 75 degrees.

Since angle a is on the opposite side of an angle with a known measure of 30º, that means angle a is vertical to it, and vertical angles both have the same measurement.
So angle a is 30º.
Since angle a and b are in a right triangle, that means we know 2 angles from that triangle and can find angle b.
Since the right triangle has a measure of 90º in its corner and we know angle a is 30º, we can add 30º and 90º then subtract this from 180º to get the measure of angle b, since all triangles' angles add up to 180º.
30 + 90 = 120
180 - 120 = 60
So angle b is 60º.
Angle c is a supplementary angle with the known angle of 75º.
Supplementary angles are angles that add up to 180º and form a straight line.
To find angle c, just subtract 75º from 180º.
180 - 75 = 105
So angle c is 105º.

Answers:
Angle A- 30º
Angle B- 60º
Angle C- 105º

Hello! i hope this
since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.