Respuesta :

Hrishii

Answer:

x = 63

Step-by-step explanation:

  • In [tex]\odot \:O, [/tex] ML and MN are tangents from external points M at points L and N respectively. OL and ON are radii of the circle.

  • [tex]\implies ML\perp OL,\:\&\: MN \perp ON[/tex] (By tangent theorem)

  • [tex]\implies m\angle MLO = m\angle MNO = 90\degree[/tex]

  • [tex]m\angle LON = 117\degree[/tex] (Given)

  • In quadrilateral LMNO, by interior angle sum theorem, we have:

  • [tex] m\angle LON+m\angle MOL +m\angle MON +m\angle LMN= 360\degree[/tex]

  • [tex] \implies 117\degree+90\degree +90\degree +x\degree= 360\degree[/tex]

  • [tex] \implies 297\degree+x\degree= 360\degree[/tex]

  • [tex] \implies x\degree= 360\degree-297\degree[/tex]

  • [tex] \implies x\degree= 63\degree[/tex]

  • [tex] \implies\red{\boxed{\bold{ x= 63}}}[/tex]

Answer:

63°

Step-by-step explanation:

  • The central angle is 117°
  • The angles at the tangent are 90° each (property of tangents)

Applying the Angle Sum of Quadrilaterals,

  • 117° + 2(90°) + x° = 360°
  • 180° + x° = 243°
  • x° = 63°