Question

let (mangle kijcong mangle jih), (mangle jih=(4x + 3)^{circ}), and (mangle kih=(12x)^{circ}). (mangle kih=__^{circ})

Explanation:

Step1: Use angle - addition property

Since $\angle KIH=\angle KIJ+\angle JIH$ and $\angle KIJ = \angle JIH=(4x + 3)^{\circ}$, then $\angle KIH=(4x + 3)+(4x + 3)=8x+6$.

Step2: Set up an equation

We know that $\angle KIH=(12x)^{\circ}$, so we set up the equation $12x=8x + 6$.

Step3: Solve the equation for $x$

Subtract $8x$ from both sides: $12x-8x=8x + 6-8x$, which gives $4x=6$. Then divide both sides by 4: $x=\frac{6}{4}=\frac{3}{2}$.

Step4: Find the measure of $\angle KIH$

Substitute $x = \frac{3}{2}$ into the expression for $\angle KIH=(12x)^{\circ}$. So $\angle KIH=12\times\frac{3}{2}=18^{\circ}$.

Answer:

$18$