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Rishi Duran
Mathematics
7 November, 10:25
What is mArc B C? 50° 80° 100° 130°
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Reynaldo Bryant
7 November, 10:53
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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°.
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