Question

Find measure FGH circles unit

Answer 1

`\huge \orange{m\widehat {FGH} =238\degree}`

Explanation:

• Quadrilateral AFGH is inscribed in a circle.
• So, it is a cyclic quadrilateral.
• Opposite angles of a cyclic quadrilateral are supplementary.

`\therefore m\angle FGH + m\angle FAH = 180\degree`

`\therefore (21x-2)\degree + (38x +5)\degree = 180\degree`

`\therefore (21x-2+38x +5)\degree = 180\degree`

`\therefore 59x+3= 180`

`\therefore 59x= 180-3`

`\therefore 59x= 177`

`\therefore x= (177)/(59)`

`\therefore x=3`

Now, by inscribed angle theorem:

`m\angle FAH = (1)/(2) m\widehat {FGH}`

`(38x +5)\degree = (1)/(2) m\widehat {FGH}`

`2(38* 3+5)\degree = m\widehat {FGH}`

`2(119)\degree = m\widehat {FGH}`

`238\degree = m\widehat {FGH}`

`\huge \purple {\boxed {m\widehat {FGH} =238\degree}}`