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Question: Find the angle measures of the inscribed quadrilateral.

Please Help I Will Award Brainliest Question Find The Angle Measures Of The Inscribed Quadrilateral class=

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Answer:

[tex] m\angle A = 112 \degree [/tex]

[tex] m\angle B=95 \degree [/tex]

[tex] m\angle C =68 \degree [/tex]

[tex] m \angle D = 85 \degree [/tex]

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle. So, ABCD is a cyclic Quadrilateral.

Opposite angles of cyclic quadrilateral are supplementary.

Therefore,

[tex]m\angle A + m\angle C = 180\degree \\ (14z - 7) \degree + (8z) \degree = 180 \degree \\ (14z - 7 + 8z) \degree= 180 \degree \\ (22z - 7) \degree= 180 \degree \\ 22z - 7 = 180 \\ 22z= 187 \\ z = \frac{187}{22} \\ z = 8.5 \\ \\ m\angle A = (14z - 7) \degree \\ = (14 \times 8.5 - 7) \degree \\ = (119 - 7) \degree \\ m\angle A = 112 \degree \\ \\ m\angle C =180 \degree - 112 \degree \\ m\angle C =68 \degree \\ \\ m \angle D = (10 \times 8.5) \degree \\ m \angle D = 85 \degree \\ \\ m\angle B =180 \degree - 85 \degree \\ m\angle B=95 \degree [/tex]

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