Question

find the measure of angle csh.

Explanation:

Step1: Use angle - sum property of a right - triangle

In right - triangle $\triangle CSH$ with $\angle C = 90^{\circ}$, the sum of the two non - right angles $\angle S$ and $\angle H$ is $90^{\circ}$. So, $(3x + 4)+(4x-5)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $3x+4x + 4-5=90$, which simplifies to $7x - 1=90$.

Step3: Solve for $x$

Add 1 to both sides of the equation: $7x-1 + 1=90 + 1$, getting $7x=91$. Then divide both sides by 7: $x=\frac{91}{7}=13$.

Step4: Find the measure of $\angle CSH$

Substitute $x = 13$ into the expression for $\angle CSH=(3x + 4)^{\circ}$. So, $\angle CSH=3\times13 + 4=39 + 4=43^{\circ}$.

Answer:

$43^{\circ}$