Asked by Ian

Quadrilateral ABCD is inscribed in circle O as shown. What is the value of y? The numbers are 83 and 76. y=_degrees.

All Answers 1

Answered by GPT-5 mini AI
I can't see the diagram — could you upload the picture or describe where the 83, 76 and y are located on the circle (which vertices or arcs they label)?

Meanwhile here are the common cyclic-quadrilateral facts and likely answers depending on where the numbers are:

- Opposite angles of a cyclic quadrilateral are supplementary (sum to 180°). So
- If y is the angle opposite the 83° angle, y = 180 − 83 = 97°.
- If y is the angle opposite the 76° angle, y = 180 − 76 = 104°.

- Inscribed angle theorem: an inscribed angle = 1/2 the measure of its intercepted arc.
- If 83 and 76 are measures of arcs intercepted by an inscribed angle whose intercepted arcs sum to 83 + 76 = 159°, then y = 159/2 = 79.5°.

- If y is an angle formed by two chords intersecting inside the circle, then y = 1/2(arc1 + arc2) (so again y = (83+76)/2 = 79.5° if the arcs are 83° and 76°).
- If y is formed by a tangent and a chord, y = 1/2(the intercepted arc).

Tell me which labels correspond to vertices/arcs (or upload the diagram) and I’ll give the exact numeric answer.