AB is tangent to the circle k(O) at B, and

AD is a secant, which goes through O. Point O is between A and D∈k(O). Find m∠BAD and m∠ADB, if measure of arc BD is 110°20'.

m∠BAD is 20° 20'

m∠ADB is 34° 50'

Step-by-step explanation:

Look to the attached figure

In circle O

∵ AB is a tangent to circle O at B

∵ AD is a secant intersects circle O at C and D

∵ O ∈ AD

- That means AD divides the circle into two equal arc

∵ The measure of the circle is 360°

∴ m of ARC CBD = × 360° = 180°

To find m∠BAD use the first rule above

∵ m∠BAD = (m arc BD - m arc BC)

∵ m arc BD = 110° 20'

- Subtract the m of arc BD from 180° to find m of arc BC

∴ m arc BC = 179° 60' - 110° 20' = 69° 40'

- Substitute the measures of arcs BD and BC in the formula

   of m∠BAD

∴ m∠BAD = (110° 20' - 69° 40') = (109° 80' - 69° 40')

∴ m∠BAD = (40° 40')

∴ m∠BAD = 20° 20'

∵ ∠ADB is an inscribed angle subtended by arc BC

- By using the 2nd rule above

∴ m∠ADB = m arc BC

∵ m arc BC = 69° 40'

∴ m∠ADB = (69° 40') =   (68° 100')

∴ m∠ADB = 34° 50'

answer: -8.2562234e+13

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step-by-step explanation: