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

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

Step2: Recall 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 $28 + 2x=180$.

Step4: Solve for x

First, subtract 28 from both sides: $2x=180 - 28=152$. Then divide both sides by 2: $x=\frac{152}{2}=76$.

Answer:

76