Question

Angle BCD is a circumscribed angle of circle A. Angle BCA measures 40°.

Circle A is shown. Line segments B A and D A are radii. Tangents B C and D C intersect at point C outside of the circle. A line is drawn to connect points A and C. Angle B C A is 40 degrees.

What is the measure of minor arc BD?

40°
50°
80°
100°

Answer 1

Answer:

D. 100

Step-by-step explanation:

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Answer 2

Based on the calculations, the measure of minor arc BD is equal to 100°.

Given the following data:

• Angle BCA = 40°.

What is a line segment?

A line segment can be defined as a part of a line that is bounded by two (2) distinct points and has a fixed length.

Based on the information given, we can deduce the following:

Angle BAD = 2(BCA)

Angle BAD = $2\times 40$

Angle BAD = 80°.

Also, angle ABC and ADC both have a measure of 90 degrees because angle BCD is a circumscribed angle.

Note: The sum of the interior angles in a quadrilateral is equal to 360°.

$ABC + ADC + BAD + BCD = 360\\\\90+90+ BAD + BCD = 360\\\\180+ BAD + BCD = 360\\\\BAD + BCD = 360-180\\\\BAD + BCD = 180$

For the minor arc BD:

$BCD =180-BAD\\\\BCD =180-80$

Angle BCD = 100°.

Read more on line segment here: brainly.com/question/18315903