line segment gj is a diameter of circle l. angle k measures (4x + 6)°. what is the value of x? 21 24 32 44

Explanation:

Step1: Recall the inscribed - angle theorem

An angle inscribed in a semi - circle is a right angle. Since line segment GJ is a diameter of circle L, angle K is an inscribed angle in a semi - circle, so angle K = 90°.

Step2: Set up the equation

We know that angle K measures (4x + 6)°. Set 4x+6 equal to 90. So, 4x + 6=90.

Step3: Solve the equation for x

Subtract 6 from both sides of the equation: 4x=90 - 6, 4x=84. Then divide both sides by 4: x = $\frac{84}{4}$, x = 21.

Answer:

21