Question

find the measure of ∠rsq. m∠rsq = °

Explanation:

Step1: Identify angle - relationship

Since $\angle RSO$ and $\angle RSQ$ are a linear - pair of angles, $\angle RSO+\angle RSQ = 180^{\circ}$. Also, $\angle RSO$ and the angle with measure $(5x + 86)^{\circ}$ are vertical angles, so $\angle RSO=(5x + 86)^{\circ}$. Then we have the equation $(5x + 86)+(10x + 46)=180$.

Step2: Solve the equation for $x$

Combine like - terms: $5x+10x+86 + 46=180$, which simplifies to $15x+132 = 180$. Subtract 132 from both sides: $15x=180 - 132=48$. Then divide both sides by 15: $x=\frac{48}{15}=\frac{16}{5}=3.2$.

Step3: Find the measure of $\angle RSQ$

Substitute $x = 3.2$ into the expression for $\angle RSQ$, which is $10x + 46$. So $\angle RSQ=10\times3.2+46=32 + 46=78^{\circ}$.

Answer:

$78$