Respuesta :

Answer:

[tex]\boxed{\bf \angle B = 58^{o}}[/tex]

Step-by-step explanation:

The cyclic quadrilateral sum of the opposite angle is 180°. From the given figure....

[tex]\bf \angle B + \angle D= {180}^{o} [/tex]

Where....

~[tex]\bf \angle B = 3x+7[/tex]

~[tex]\bf \angle D = 6x+20[/tex]

  • [tex]\bf 3x+7+6x+20 ={180}^{o} [/tex]
  • [tex]\bf 9x+27=180^{o}[/tex]
  • [tex]\bf 9x=180-27[/tex]
  • [tex]\bf 9x=153[/tex]
  • [tex]\bf x = \cfrac{153}{9} [/tex]
  • [tex]\boxed{\bf x=17^{o}}[/tex]

Now, that we found x, let's find angle B....

  • [tex]\bf \angle \: B = 3x + 3[/tex]
  • [tex]\bf 3(17) + 7[/tex]
  • [tex]\bf 58^{o}[/tex]

[tex]\sf Therefore, \: \boxed{\sf \angle B = 58^{o}}[/tex]

ACCESS MORE
EDU ACCESS