Question

what is the value of x? k j 3x + 24° i x =

Explanation:

Step1: Identify the triangle properties

Since $IK = IJ$ (marked with equal - side symbols), $\triangle IKJ$ is isosceles. So, the base - angles are equal. Let the base - angles be $\angle K=\angle J = 3x + 24^{\circ}$. Also, since $KJ$ is a diameter of the circle, the angle inscribed in a semi - circle $\angle KIJ=90^{\circ}$.

Step2: Use the angle - sum property of a triangle

In $\triangle IKJ$, the sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle K+\angle J+\angle KIJ = 180^{\circ}$. Substitute the values: $(3x + 24^{\circ})+(3x + 24^{\circ})+90^{\circ}=180^{\circ}$.

Step3: Simplify the equation

Combine like terms: $6x+24^{\circ}+24^{\circ}+90^{\circ}=180^{\circ}$, which simplifies to $6x + 138^{\circ}=180^{\circ}$.

Step4: Solve for x

Subtract $138^{\circ}$ from both sides: $6x=180^{\circ}-138^{\circ}=42^{\circ}$. Then divide both sides by 6: $x = 7^{\circ}$.

Answer:

$7$