Question

40 (pts)

show work and answer(not multiple choice)
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle Q? You must show all work and calculations to receive credit.

Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2x plus 4 degrees. R is labeled 3y plus 8 degrees.

Answer 1

m<Q = 92 degrees

Explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary.

Angles O and Q are opposite angles, so they are supplementary, so their measures add up to 180 degrees.

m<O + m<Q = 180

2x + 2x + 4 = 180

4x + 4 = 180

4x = 176

x = 44

m<Q = 2x + 4 = 2(44) + 4 = 92

Answer 2

Q =92

Explanation:

Since the quadrilateral is inscribed in a circle, the opposite angles add to 180 degrees.

<O + <Q = 180

2x+ 2x+4 = 180

4x+4 =180

Subtract 4 from each side

4x= 180-4

4x= 176

Divide by 4

x = 44

Q = 2x+4

Q = 2(44)+4

Q = 88+4

Q = 92