What is mArc B C? 50° 80° 100° 130°

130

Step-by-step explanation:

The measurement of arc BC is 130°.

Step-by-step explanation:

Given : circle with origin O, with two line segments AC and BD which are also diameters.

Measurement of arc AB = (3 x - 70) ° =

Measurement of arc DC = (x + 10) ° = ∠3

To find : Measurement of arc BC = ∠2 = ?

Solution:

Let angle subtended by the arc AC = ∠1 = (3 x - 70) °

Let angle subtended by the arc BD = ∠2

Let angle subtended by the arc DC = ∠3 = (x + 10) °

Let angle subtended by the arc AD = ∠4

AC and BD are intersecting each other at O.

So, ∠1 = ∠3 (vertically opposite angles) ... [1]

∠2 = ∠4 (vertically opposite angles) ... [2]

(3 x - 70) ° = (x + 10) ° (from [1])

3x - x = 10 + 70

∠1 = ∠3 = (x + 10) ° = (40 + 10) ° = 50°

∠1 + ∠2 + ∠3 + ∠4 = 360°

50° + ∠2 + 50° + ∠2 = 360° (from [2])

2∠2 = 360° - 50° - 50°

2∠2 = 260°

∠2 = 260° : 2

∠2 = 130°

The measurement of arc BC is 130°.