Question

find the value of x. the diagram is not to scale. given: ∠srt≅∠str, m∠srt = 28, m∠stu = 2x

Explanation:

Step1: Use angle - equality property

Since $\angle SRT\cong\angle STR$ and $m\angle SRT = 28$, then $m\angle STR=28$.

Step2: Use linear - pair property

$\angle STR$ and $\angle STU$ form a linear - pair. So $m\angle STR + m\angle STU=180$.

Step3: Substitute values

Substitute $m\angle STR = 28$ into $m\angle STR + m\angle STU=180$, we get $28 + m\angle STU=180$. Then $m\angle STU=180 - 28=152$.

Step4: Solve for x

Given $m\angle STU = 2x$, then $2x=152$. Divide both sides by 2: $x=\frac{152}{2}=76$.

Answer:

76