Given: tangents la and lb m∠aob=110°

find: m∠alo.

35°

Step-by-step explanation:

From any point outside a circle, the two tangents to that circle are always congruent to each other. This can be proven by taking the two triangles ΔLAO and ΔLBO and prove that they are congruent. From the upper triangle AO is congruent to BO because AO = BO = Radius. Also, LO is the same length for both triangles, therefore two equal sides. Moreover, the measure of an angle between the tangent to a point of the circle and the radius going from the center to that point equals 90°, so ∠LAO = ∠LBO = 90°. So these two triangles ΔLAO and ΔLBO are congruent by SSA postulate.

If m∠AOB=110°, then m∠AOL = 110°/2 =55°. Finally, the angles of every triangle always measures 180°, therefore:

m∠ALO = 180°-55°-90 = 35°