Given: Tangents
LA
and
LB
m∠AOB=110°
Find: m∠ALO.

Answer:
m<ALO=35°
Step-by-step explanation:
we know that
The right triangle AOL is congruent with the right triangle BOL
because
OA=OB=radius of the circle
OL is a common side
LA=LB ---> by applying the Pythagoras theorem
therefore
m<AOL=m<AOB/2
m<AOL=110°/2
m<AOL=55°
Remember that
m<AOL+m<ALO=90° ------> by complementary angles
m<ALO=90°-55°=35°