Question

question find m∠rcb if m∠dcr = 58°, m∠rcb = 28x - 2, and m∠dcb = 42x

Explanation:

Step1: Use angle - addition postulate

Since $\angle DCB=\angle DCR+\angle RCB$, we can substitute the given angle - measures: $42x = 58+(28x - 2)$.

Step2: Simplify the right - hand side of the equation

First, simplify $58+(28x - 2)$ to $28x+56$. So the equation becomes $42x=28x + 56$.

Step3: Solve for $x$

Subtract $28x$ from both sides: $42x-28x=28x + 56-28x$. This gives $14x=56$. Then divide both sides by 14: $x=\frac{56}{14}=4$.

Step4: Find $m\angle RCB$

Substitute $x = 4$ into the expression for $m\angle RCB$. We have $m\angle RCB=28x-2=28\times4-2=112 - 2=110^{\circ}$.

Answer:

$110^{\circ}$