Question

Find the measure indicated. Assume that the lines which appear to be tangent are tangent. Part 4

NO LINKS OF ANY KIND
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Answer 1

The angle between the two tangents drawn from an external point to a circle and the angle subtended by the line segment joining the points of the contact at the Centre are supplymentary,

So,

15.) let the unknown angle be x

=》x + 55° = 180°

=》x = 180° - 55°

=》

`\boxed{x = 125°}`

16. let the unknown angle be n

=》n + 80° = 180°

=》n = 180° - 80°

=》

`\boxed{n = 100°}`

Answer 2

9514 1404 393

Answer:

15) 125°

16 100°

Explanation:

The short arc where two tangents intersect a circle, and the angle where the tangents meet are supplementary.

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15) ? = 180° -55° = 125°

16) ? = 180° - 80° = 100°

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Additional comment

The quadrilateral formed by the tangents and the radii to the points of tangency has a total interior angle measure of 360°. The angles where the radii meet the tangents are 90°, so the sum of the external angle and the central angle is 360° -90° -90° = 180°. That is, the external angle and the central angle are supplementary.