Respuesta :

Answer:

b.  26°

Step-by-step explanation:

ABE is tangent to the circle then m∡OBE = m∡OBD = 90

Then m∡OBD = 90 - 58 = 32

In the triangle DAB :

m∡CAB = m∡DAB = 180 - [m∡BDA + (m∡DBA)]

                                = 180 - [     32       + (90 + 32)]

                                = 180 - [     32       + ( 122) ]      

                                = 180 - [ 154 ]    

                                = 26                    

Answer:

B) 26°

Step-by-step explanation:

Finding ∠OBD

  • ∠OBA = ∠OBE = 90° [tangent to the circle]
  • ∠OBE - 58° = ∠OBD
  • ∠OBD = 90° - 58°
  • ∠OBD = 32°

Then, ∠ADB = ∠OBD = 32° (angles opposing equal sides OB and OD, both of which are radii of the circle.

Finding ∠CAB

  • ∠CAB + ∠ADB + ∠OBD + ∠OBA = 180° [Angle Sum Property]
  • ∠CAB + 32° + 32° + 90° = 180°
  • ∠CAB + 154° = 180°
  • ∠CAB = 26°

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