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a = 50°, b = 130°, c = 20°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles in the right triangle

a + 40° + 90° = 180°

a + 130° = 180° ( subtract 130° from both sides )

a = 50°

a and b are adjacent angles and sum to 180° , so

a + b = 180°

50° + b = 180° ( subtract 50° from both sides )

b = 130°

Then sum the angles in the top triangle, that is

30° + 130° + c = 180°

160° + c = 180° ( subtract 160° from both sides )

c = 20°

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

d. 145*2 is 290 than the total angle is 360 then minus 290 then divide by two