Question

HELP ANWSER ASAP PLEASE

Answer 1

`\boxed{x = 45°}`

Explanation:

When two chords intersect at a point in a circle, they form arcs, along with angles at the intersection point.

To determine the angle of the arc, we must apply this geometric rule:

`Angle \: formed \: by \: chords = (1)/(2)(sum \: of \: intersecting \: arcs)`.

Since we are looking for one of the arcs, we can rearrange this formula to solve for the first arc.

`Angle \: formed \: by \: chords = (1)/(2)(sum \: of \: intersecting \: arcs)` →

`Angle \: formed \: by \: chords = (1)/(2)(\overset{\frown}{BA} + \overset{\frown}{CD})` →

`2 × Angle \: formed \: by \: chords = \overset{\frown}{BA} + \overset{\frown}{CD}` →

`2 × Angle \: formed \: by \: chords \: – \: \overset{\frown}{CD} = \overset{\frown}{BA}`

`\overset{\frown}{BA} = 2 × Angle \: formed \: by \: chords \: – \: \overset{\frown}{CD}`

[Given]

`\overset{\frown}{BA} = x°`

`\overset{\frown}{CD} = 99°`

`Angle \: formed \: by \: chords \: = 72°`

→

`\overset{\frown}{BA} = 2 × Angle \: formed \: by \: chords \: – \: \overset{\frown}{CD}`

→

`x° = 2 × 72° \: – \: 99°`

`x° = (2 × 72°) \: – \: 99°`

`x° = 144° \: – \: 99°`

`\boxed{x° = 45°}`