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 40 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 65 degrees.

Hello!

First of all, angles a and 40 are vertical angles, as they are opposite from each other and their points touch. This means they are congruent.

Therefore, ∠a=40°.

Now we need to find b. As we already have angle A in our little triangle, which is 40°, and a 90° angle, we subtract from 180° to find b.

180-40-90=50

Therefore, ∠b=50°.

Now we need to find angle c. As you can see, c and 65 make a straight, or 180° angle. This means they are supplementary and that their angle measures add up to 180. We can then find c below.

180-65=115

Therefore, ∠c=115°

I hope this helps!