Question

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

Explanation:

Step1: Recall the inscribed - angle theorem

An angle inscribed in a semi - circle is a right angle. So, angle $K = 90^{\circ}$.

Step2: Set up the equation

We know that $\angle K=(4z + 6)^{\circ}$, and $\angle K = 90^{\circ}$. So, we set up the equation $4z+6 = 90$.

Step3: Solve the equation for $z$

Subtract 6 from both sides: $4z=90 - 6=84$. Then divide both sides by 4: $z=\frac{84}{4}=21$.

Answer:

21