PLZ HELP ASAP TANGENTS OF CIRCLES

Mathematics

1 answer:

bezimeni [28]2 years ago

7 0

First, we are given that the inscribed angle of arc CB which is angle D is equal to 65°. This is half of the measure of the arc which is equal to the measure of the central angle, ∠O.

m∠O = 2 (65°) = 130°

Also, the measure of the angles where the tangent lines and the radii meet are equal to 90°. The sum of the measures of the angle of a quadrilateral ACOB is equal to 360°.

m∠O + m∠C + m∠B + m∠A = 360°

Substituting the known values,
130° + 90° + 90° + m∠A = 360°

The value of m∠A is equal to 50°.

<em>Answer: 50°</em>

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