Question

Circle O is shown. Line segments A C and B D are diameters. The measure of arc A B is (3 x minus 70) degrees and the measure of arc D C is (x + 10) degrees. What is mArc B C? 50° 80° 100° 130° In circle O, AC and BD are diameters. In circle O, AC and BD are diameters.

Answer 1

Answer:

Option (4)

Step-by-step explanation:

From the given circle O,

AC and BD are the diameters intersecting at point O.

∠AOB ≅ ∠COD [Vertical angles]

Therefore, length of intercepted arcs by these central angles will be same.

$m(\widehat{AB})=m(\widehat{CD})$

(3x - 70) = (x + 10)

3x - x = 70 + 10

2x = 80

x = 40

Since, $m(\widehat{AB})+m(\widehat{BC})=180$ [Since AC is a diameter]

(3x - 70) + $m(\widehat{BC})$ = 180°

3(40) - 70 + $m(\widehat{BC})$ = 180°

$m(\widehat{BC})$ = 180° - 50°

           = 130°

Therefore, Option (4) will be the correct option.