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# inscribed angles 2

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2
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​ Quadrilateral ABCD ​ is inscribed in this circle.

What is the measure of angle B?

AgentFatboy  Mar 23, 2018

#1
+12235
+2

OPPOSITE angles of a cyclic quadrilateral ( a quadrilateral with all vertices on the circumference of a given circle) add to 180 degrees.....s o

x + (4x-20) = 180

5x=200

x = 40

B = 4x-20

4(40) - 20 = 140 degrees

ElectricPavlov  Mar 23, 2018
Sort:

#1
+12235
+2

OPPOSITE angles of a cyclic quadrilateral ( a quadrilateral with all vertices on the circumference of a given circle) add to 180 degrees.....s o

x + (4x-20) = 180

5x=200

x = 40

B = 4x-20

4(40) - 20 = 140 degrees

ElectricPavlov  Mar 23, 2018
#2
0

The opposite angles of a cyclic quadrilateral (a quadrilateral whose vertices touch the circumference of a circle) always add up to 180°.

Thus:

$$x+4x-20=180$$

$$5x-20=180$$

$$5x=180+20=200$$

$$x=\frac { 200 }{ 5 } =40$$

$$\angle B=(4x-20)°=(4\times 40-20)°=(160-20)°=140°$$

So, the measure of angle B is 140°.

Guest Mar 24, 2018

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