Circle L is inscribed with triangle G J K. Line segment G J is a diameter. Line segments G K and K J are secants. Angle K has a measure of (4x + 6) degrees. What is the value of x?
21,  24,  32, 44

Solution:

We observe that

The secant GJ is the diameter and K is the angle that is subtended by the diameter on the circumference of the circle.

We know that the angle inscribed in a semicircle is 90⁰ 

∠K = 90⁰

Thus we have

4x + 6 = 90⁰

Subtract 6 from both sides

4x + 6 - 6 = 90 - 6

4x = 84

Divide both sides by 4

4x/4 = 84/4

x = 21

Hence, the value of x is 21.

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Circle L is inscribed with triangle G J K. Line segment G J is a diameter. Line segments G K and K J are secants. Angle K has a measure of (4x + 6) degrees. What is the value of x?

Summary:

Circle L is inscribed with triangle G J K. Line segment G J is a diameter. Line segments G K and K J are secants. Angle K has a measure of (4x + 6) degrees. The value of x is 21.