Question

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what is m∠cdj?
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Explanation:

Step1: Set up equation using angle - sum property

Since $\angle CDJ$ is a right - angle (as indicated by the small square at the intersection), the sum of the two given angles $(4x)^{\circ}$ and $(3x - 8)^{\circ}$ is $90^{\circ}$. So, $4x+(3x - 8)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $4x+3x-8 = 90$, which gives $7x-8 = 90$.

Step3: Solve for $x$

Add 8 to both sides of the equation: $7x-8 + 8=90 + 8$, so $7x=98$. Then divide both sides by 7: $x=\frac{98}{7}=14$.

Step4: Find the measure of $\angle CDJ$

Substitute $x = 14$ into the expression for $\angle CDJ$. The measure of $\angle CDJ=(4x+(3x - 8))^{\circ}$. Substituting $x = 14$, we have $4\times14+(3\times14 - 8)=56+(42 - 8)=56 + 34=90$.

Answer:

$90$