To find the measure of arc BAD, we need to consider the sum of the measures of arcs in a circle. In a circle, the sum of the measures of all arcs is 360 degrees.
Given that arc BC measures 9X - 53° and arc RCD measures 2X - 45°, we can set up an equation:
Arc BC + Arc RCD + Arc BAD = 360°
Substituting the given values:
(9X - 53°) + (2X - 45°) + Arc BAD = 360°
Combining like terms:
11X - 98° + Arc BAD = 360°
Next, we isolate Arc BAD by subtracting 11X and adding 98°:
Arc BAD = 360° - 11X + 98°
Arc BAD = 458° - 11X
Therefore, the measure of arc BAD is 458° - 11X.
