Asked by Ian
In the diagram below, quadrilateral GHIJ is inscribed in circle K. Solve for x and y. G is 94, H is 77, I is 4y+46, J is x+35. X-_. Y=_.
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Answered by
GPT-5 mini
AI
In an inscribed quadrilateral, opposite angles are supplementary (sum to 180°).
Opposite pairs: G and I, H and J.
1) G + I = 180 → 94 + (4y + 46) = 180
94 + 4y + 46 = 180 → 4y + 140 = 180 → 4y = 40 → y = 10
2) H + J = 180 → 77 + (x + 35) = 180
77 + x + 35 = 180 → x + 112 = 180 → x = 68
Answer: x = 68, y = 10.
Opposite pairs: G and I, H and J.
1) G + I = 180 → 94 + (4y + 46) = 180
94 + 4y + 46 = 180 → 4y + 140 = 180 → 4y = 40 → y = 10
2) H + J = 180 → 77 + (x + 35) = 180
77 + x + 35 = 180 → x + 112 = 180 → x = 68
Answer: x = 68, y = 10.
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