Question

What is the value of c?

Answer 1

Theorem: If a quadrilateral is inscribed in a circle, then opposite angles of the quadrilateral are supplementary.

The a degree angle and the 68 degree angle are opposite.

a + 68 = 180
a = 112

Answer 2

The angle with measure a is an inscribed angle of a circle.

Theorem: The measure of an inscribed angle of a circle is 1/2 of its intercepted arc.

The angle with measure a intercepts an arc (see attached diagram) with measure (b + 104).

Answer 3

Oops I meant finding c would you go through the same process

Answer 4

That gives an equation to solve:

112 = 1/2 * (b + 104) @jadesterxx Solve for b and post what you get, okay?

Answer 5

60? @Directrix

Answer 6

60 is not correct.

Does 112 = 1/2 * (60 + 104) ?

1/2 of 164 = 82 and not 112

Answer 7

Oh okay I got 120?

Answer 8

@Directrix

Answer 9

So, you changed the problem from b to c.

Answer 10

The angle opposite the 71 degree angle has measure 109 because those two angles are supplementary.

Answer 11

The 109 degree angle is also an inscribed angle of a circle.

109 = 1/2 * (120 + x) @jadesterxx Solve for x.
After that, one short subtraction step to c.

Answer 12

Solve this for x is your task.

109 = 1/2 * (120 + x)

Answer 13

x = 98
To get c,

solve this:

104 + 120 + 98 + c = 360 (360 degrees in a circle)

Answer 14

@jadesterxx ^^^

Answer 15

So it would be 38?

Answer 16

That is what I got for the measure of arc c.

Answer 17

Thanks a lot! It really helped

Answer 18

You are welcome.

Answer 19

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