Question

what is m∠ikj? m∠ikj = °

Explanation:

Step1: Recall central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Here, the central angle $\angle{JHI}=3x + 75^{\circ}$ and the inscribed angle $\angle{IKJ}=3x$.
We know that $3x=\frac{1}{2}(3x + 75^{\circ})$.

Step2: Solve the equation for $x$

Multiply both sides of the equation $3x=\frac{1}{2}(3x + 75^{\circ})$ by 2 to get $6x=3x + 75^{\circ}$.
Subtract $3x$ from both sides: $6x-3x=3x + 75^{\circ}-3x$.
So, $3x = 75^{\circ}$, and then $x = 25^{\circ}$.

Step3: Find the measure of $\angle{IKJ}$

Since $\angle{IKJ}=3x$, substitute $x = 25^{\circ}$ into the expression.
$\angle{IKJ}=3\times25^{\circ}=75^{\circ}$.

Answer:

$75$