Answer:
28°
Explanation:
You want the measure of exterior angle BCD formed by tangents BC and DC to circle O, where inscribed angle DFB is 76°.
Inscribed angle
The inscribed angle is half the measure of the arc it intercepts.
1/2(arc BD) = angle DFB
arc BD = 2(angle DFB) = 2(76°) = 152°
Exterior angle
An exterior angle is the supplement of the central angle between the radii to the tangent points. The central angle has the same measure as the arc it intercepts.
angle BCD = 180° -angle DOB
angle BCD = 180° -152° = 28°
The size of angle BCD is 28°.
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Additional comment
If your teacher gets a different answer, you should have them show you their work.
The attached diagram is drawn to scale.
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