Question

Can you help me solve this equation? 20 POINTS

Answer 1

63°

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°

Answer 2

x = 63

Explanation:

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

• 
  `\implies ML\perp OL,\:\&\: MN \perp ON` (By tangent theorem)

• 
  `\implies m\angle MLO = m\angle MNO = 90\degree`

• 
  `m\angle LON = 117\degree` (Given)

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

• 
  `m\angle LON+m\angle MOL +m\angle MON +m\angle LMN= 360\degree`

• 
  `\implies 117\degree+90\degree +90\degree +x\degree= 360\degree`

• 
  `\implies 297\degree+x\degree= 360\degree`

• 
  `\implies x\degree= 360\degree-297\degree`

• 
  `\implies x\degree= 63\degree`

• 
  `\implies\red{\boxed{\bold{ x= 63}}}`