Find the angle measure indicated. Assume that lines which appear to be tangent are tangent.

Solution:

We know that the length of tangents which are drawn from an external point are equal.

PA = PB

The tangent at any point on the circle is perpendicular to the radius of the circle through the point of contact.

OB ⊥ PB and OA ⊥ PA

∠PBO = 90°, ∠PAO = 90°

The sum of all the angles in a quadrilateral is 360°.

In the quadrilateral PAOB

∠APB + ∠PAO + ∠PBO + ∠AOB = 360°

43° + 90° + 90° + ∠AOB = 360°

∠AOB = 360° - 223°

∠AOB = 137°

Therefore, the angle measure indicated is 137°.

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Find the angle measure indicated. Assume that lines which appear to be tangent are tangent.

Summary:

The angle measure indicated is 137°.The tangent at any point on the circle is perpendicular to the radius of the circle through the point of contact.