Question

ASAP Help me please!!

Answer 1

Answer:  x = 14

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Work Shown:

Refer to the diagram below. I've added a line segment and two variables y and z. This forms two isosceles triangles.

The central angle 56 degrees subtends the same arc as the inscribed angle y. By the inscribed angle theorem, this means y = 56/2 = 28. The inscribed angle is always half of the central angle (when both angles subtend the same arc).

Focus on the smaller isosceles triangle that has angles 56, z and z. Those three angles add to 180

z+z+56 = 180

2z+56 = 180

2z = 180-56

2z = 124

z = 124/2

z = 62

Now focus on the larger isosceles triangle (angles y = 28, x+z and x+z)

We'll use the same trick as before.

(x+z)+(x+z)+(y) = 180

(x+62)+(x+62)+(28) = 180 ... plug in z = 62 and y = 28

2x+152 = 180

2x = 180-152

2x = 28

x = 28/2

x = 14