Question

find the measure of ∠knh. m∠knh =

Explanation:

Step1: Identify angle - relationship

Since $\angle KNH$ and the angle with measure $(25x)^{\circ}$ are corresponding angles (assuming $IJ\parallel KL$), they are congruent. So we set up the equation $30x - 15=25x$.

Step2: Solve the equation for $x$

Subtract $25x$ from both sides: $30x-25x - 15=25x-25x$, which simplifies to $5x-15 = 0$. Then add 15 to both sides: $5x-15 + 15=0 + 15$, getting $5x=15$. Divide both sides by 5: $x=\frac{15}{5}=3$.

Step3: Find the measure of $\angle KNH$

Substitute $x = 3$ into the expression for $\angle KNH$ which is $30x-15$. So $m\angle KNH=30\times3-15=90 - 15=75^{\circ}$.

Answer:

$75$