Question

HELP URGENT
find angle CAB
a. 32
b. 26
c. 64
d. 58

Answer 1

B) 26°

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°

Answer 2

b. 26°

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