Question

Angle measures for 10 points

Answer 1

x = 76°

y = 128°

z = 16°

Explanation:

JKLM is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

x + 104° = 180°

x = 180° - 104°

`\huge \red {\boxed {x = 76\degree}}`

y + 52° = 180°

y = 180° - 52°

`\huge \purple {\boxed {y = 128\degree}}`

By inscribed angle theorem:

`88\degree + z = 2* 52\degree \\\\</p><p></p><p>88\degree + z = 104\degree \\\\</p><p> z = 104\degree - 88\degree \\\\</p><p>\huge \orange {\boxed {z = 16\degree}}`