Question

Find measure FGH circles unit

Answer 1

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:

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

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

$2(38\times 3+5)\degree = m\widehat {FGH}$

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

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

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