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viva [34]
2 years ago
7

Find measure FGH circles unit

Mathematics
1 answer:
Tanya [424]2 years ago
3 0

Answer:

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

Step-by-step 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= \frac{177}{59}

\therefore x=3

Now, by inscribed angle theorem:

m\angle FAH = \frac{1}{2} m\widehat {FGH}

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

2(38\times 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}}

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