Question

in the diagram below of triangle $qrs$, $t$ is the mid - point of $overline{qs}$ and $u$ is the mid - point of $overline{rs}$. if $mangle sqr=-5x + 45$, and $mangle stu=-7x + 49$, what is the measure of $angle sqr$? answer $mangle sqr=square^{circ}$

Explanation:

Step1: Apply mid - point theorem

By the mid - point theorem in a triangle, $TU\parallel QR$. So, $\angle SQR=\angle STU$.

Step2: Set up the equation

Set $- 5x + 45=-7x + 49$.

Step3: Solve for x

Add $7x$ to both sides: $-5x+7x + 45=-7x+7x + 49$, which simplifies to $2x+45 = 49$. Then subtract 45 from both sides: $2x+45 - 45=49 - 45$, getting $2x=4$. Divide both sides by 2: $x = 2$.

Step4: Find the measure of $\angle SQR$

Substitute $x = 2$ into the expression for $\angle SQR$. $\text{m}\angle SQR=-5(2)+45=-10 + 45=20$.

Answer:

20