Question

Find the value of y (see picture)

82°

119.5°

75°

239°

Answer 1

Option 2: 119.5°

Explanation:

Angle corresponding to the arc with 75° makes an angle of 75/2 = 37.5° on the circumference

y is the exterior angle to the triangle shown

Exterior angle = sum of interior angles

y = 37.5 + 82 = 119.5°

Answer 2

B

Explanation:

The property we need to use here is shown in the attachment.

Applying it here, we see that the "x" arc is actually the intercepted arc of the angle labelled y, which means that the degree is 2 * y, by another property (that the measure of inscribed angle is always half of the measure of its corresponding intercepted arc).

We know that "y" arc from the equation is 75 degrees, and finally the
`(1)/(2) (x-y)` part of the equation can be written as:
`(1)/(2) (2y-75)`. We know that it's equal to 82, so set them equal and solve for y:

`(1)/(2) (2y-75)=82`

2y - 75 = 82 * 2 = 164

2y = 239

y = 239/2 = 119.5

The answer is B.

Hope this helps!