Answer:
The measure of angle ALO = 35°
Step-by-step explanation:
* Lets talk about the tangents to a circle drawn from a point 
  outside the circle:
- They are equal in length
- They are perpendicular to the radii at the point of tang-ency
- If we join the points of tang-ency withe the center of the circle
  and join the outside point with center of the circle, we 
  formed two congruent triangles
* Now lets check our problem
- AL and LB are two tangents to the circle O ant points A and B
∴ LA = LB ⇒ (1)
- OA and OB are radii in circle O
∴ OA = OB ⇒ (2)
∴ OA ⊥ AL and OB ⊥ BL ⇒ radius and tangent
∴ m∠OAL = 90° , m∠OBL = 90
∴ m∠OAL = m∠OBL ⇒ (3)
* From (1) , (2) , (3)
- The two triangles LAO and LBO are congruent ⇒ SAS
- SAS is one case of congruence
∵ The lengths of two sides and the measure of the including
   angle between them in one triangle equal to the 
   corresponding sides and angles in the second triangle,
   then the two triangles are congruent
∴ m∠LOA = m∠LOB
∵ m∠AOB = 110°
∴ m∠LOA = m∠LOB = 110/2 = 55°
* In ΔLAO
∵ m∠ LAO = 90° , m∠LOA = 55°
∴ m∠ALO = 180 - (90 + 55) = 180 - 145 = 35°
* The measure of angle ALO = 35°