Respuesta :

danielmaduroh

Answer:

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°

The straight line that "just touches" the curve at a particular location is called the tangent line to a plane curve. The measure of the ∠ALO is 35°.

What is a tangent?

The straight line that "just touches" the curve at a particular location is called the tangent line to a plane curve.

As the measure of the ∠AOB is 110°, while the line LO is bisecting the ∠AOB, therefore, the measure of the ∠AOL = ∠BOL =55°.

We know that the angle between the tangent and the radius of the circle will be equal to 90°, therefore, in the triangle AOL, the sum of all the angles of a triangle can be written as,

[tex]\angle ALO +\angle AOL + \angle LAO = 180^o\\\\\angle ALO = 180^o-90^o-55^o\\\\\angle ALO = 35^o[/tex]

Hence, the measure of the ∠ALO is 35°.

Learn more about Tangent:

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