Question

1. find m∠rsq and m∠tsq

(15x - 43)
(8x + 18)

Explanation:

Step1: Combine like - terms

Combined $x$ terms and constant terms.

Step2: Add 25 to both sides

To isolate the term with $x$.

Step3: Divide by 23

To solve for $x$.

Step4: Find $\angle RSQ$

Substitute $x$ value into $\angle RSQ$ formula.

Step5: Find $\angle TSQ$

Substitute $x$ value into $\angle TSQ$ formula.

Answer:

Let's assume that $\angle RST = 90^{\circ}$ and $\angle RSQ+\angle TSQ=\angle RST$. So, $(15x - 43)+(8x + 18)=90$.
First, solve for $x$:

Step1: Combine like - terms

$(15x+8x)+(-43 + 18)=90$
$23x-25 = 90$

Step2: Add 25 to both sides

$23x-25+25=90 + 25$
$23x=115$

Step3: Divide both sides by 23

$x=\frac{115}{23}=5$
Now, find $\angle RSQ$ and $\angle TSQ$:

Step4: Find $\angle RSQ$

Substitute $x = 5$ into the expression for $\angle RSQ$:
$\angle RSQ=15x-43=15\times5-43=75 - 43=32^{\circ}$

Step5: Find $\angle TSQ$

Substitute $x = 5$ into the expression for $\angle TSQ$:
$\angle TSQ=8x + 18=8\times5+18=40 + 18=58^{\circ}$

So, $m\angle RSQ = 32^{\circ}$ and $m\angle TSQ = 58^{\circ}$