Circle O is shown. Line segments AC and BD are diameters. The measure of arc AB is (3x minus 70) degrees and the measure of arc DC is (x + 10) degrees. What is mArc BC?

Solution:

Given, measurement of arc AB = (3x - 70)°

Measurement of arc DC = (x + 10)°

We have to find the measurement of arc BC.

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

Let the angle subtended by the arc BD = ∠2

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

Let the 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)

 Now, (3x - 70)° =  (x + 10)°

3x - x = 10 + 70

2x = 80

x = 80/2

x = 40

Now,  (3x - 70)° =  (3(40) - 70)°= (120 - 70)° = 50°

 (x + 10)° =  (4 + 10)° = 50°

So, ∠1 + ∠2 + ∠3 + ∠4 = 360°

50° + ∠2 + 50° + ∠4 = 360°

100° + ∠2 + ∠2 = 360°

2∠2 = 360° - 100°

∠2 = 260°/2

∠2 = 130°

Therefore, the measurement of arc BC is 130°.

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Circle O is shown. Line segments AC and BD are diameters. The measure of arc AB is (3x minus 70) degrees and the measure of arc DC is (x + 10) degrees. What is mArc BC?

Summary:

Circle O is shown. Line segments AC and BD are diameters. The measure of arc AB is (3x minus 70) degrees and the measure of arc DC is (x + 10) degrees, then mArc BC is 130°.