Question

The measure of arc BD is __.

The measure of arc ADB is __.
The measure of arc ABC is __.

PLEASE HELP. URGENT!! ASAP

Answer 1

BD= 100

ADB= 220

ABC= 180

Answer 2

- The measure of arc
`\( BD \)` is 260°.

- The measure of arc
`\( ADB \)` should be 320° (corrected).

- The measure of arc
`\( ABC \)` is 80°.

To find the measure of each arc in the circle, we need to remember that the total degrees in any circle is 360°. The diagram shows a circle with specific arcs and angles labeled.

Here are the steps to find each arc's measure:

1. Measure of arc
`\( BD \)`:

- Arc
`\( BD \)` is opposite the central angle
`\( \angle BRD \)`, which is not directly given.

- Since
`\( \angle BRC \)` is 40° and
`\( \angle CRD \)` is 60°, then
`\( \angle BRD = 360° - (\angle BRC + \angle CRD) \)`.

- Calculating
`\( \angle BRD \)` gives
`\( 360° - (40° + 60°) = 260° \)`.

- Therefore, the measure of arc \( BD \) is 260°.

2. Measure of arc
`\( ADB \)`:

- Arc
`\( ADB \)` includes arcs
`\( AD \)` and
`\( DB \)`.

- We already know
`\( DB \)` is 260°.

-
`\( AD \)` is opposite the central angle
`\( \angle ARD \)`, which is given as 120°.

- Adding them together, the measure of arc
`\( ADB = \angle ARD + \angle BRD = 120° + 260° = 380° \).`

- This exceeds 360°, which suggests an error. Since
`\( AD \)` and
`\( BD \)` are parts of the circle that add up to its whole circumference, they should add up to 360°, not more. Hence,
`\( ADB \)` should be
`\( 360° - \angle BCD \)` which is 360° - 40° = 320°.

3. Measure of arc
`\( ABC \)`:

- Arc
`\( ABC \)` includes arcs
`\( AB \)` and
`\( BC \).`

-
`\( BC \)` is opposite the central angle
`\( \angle BRC \)`, which is given as 40°.

-
`\( AB \)` is the rest of the circle not included in \( ADB \), so
`\( AB = 360° - \angle ADB \)`.

- Since we've found an inconsistency with
`\( ADB \)`, we should instead calculate
`\( AB \)` as
`\( 360° - (BD + CD) = 360° - (260° + 60°) = 40° \).`

- Adding \( AB \) and \( BC \), the measure of arc
`\( ABC = AB + BC = 40° + 40° = 80° \).`

There seems to be an error with the measure of arc
`\( ADB \)` as calculated before. Arcs
`\( AD \)` and
`\( DB \)` should add up to 360° because they complete the circle together. It's also worth noting that in a properly drawn circle, the sum of the measures of arcs
`\( BC \)`,
`\( CD \)`, and
`\( DA \)`should add up to 360°. If
`\( BC \)` is 40° and
`\( CD \)` is 60°, then
`\( DA \)` should be 360° - (40° + 60°) = 260°, not 120°. This discrepancy suggests there may be a mistake in the given information or a misinterpretation of the diagram.

To summarize, given the information provided:

- The measure of arc
`\( BD \)` is 260°.

- The measure of arc
`\( ADB \)` should be 320° (corrected).

- The measure of arc
`\( ABC \)` is 80°.