Chapter 2.7, Problem 9PSA

To determine

To calculate : The value of $m\angle STW$ is to be calculated

Answer to Problem 9PSA

The final value of $m\angle STW={70}^0$

Explanation of Solution

Given information : The following information has been given

  $\angle W=\angle STV$

  $\overrightarrow{TV}$ bisects $\angle STW$

  $\angle W={(2x-5)}^o$

  $\angle VTW={(x+15)}^o$

Formula used : Information/data provided in the question that are used to solve this particular category of solution/solution.

Calculation : If we know that $\angle VTW={(x+15)}^o$ , and $\overrightarrow{TV}$ bisects $\angle STW$ , then we can say that

  $\angle STV=\angle VTW={(x+15)}^o$

Now, if we also know that $\angle W=\angle STV$ , then we can say that

  $\angle STV=\angle W={(x+15)}^o$

But, we are given that $\angle W={(2x-5)}^o$

Hence, we equate both the values of $\angle W$

  ${(x+15)}^o={(2x-5)}^o$

Now, we find the value of x from the above equation. Thus, we get

  $x={20}^0$

Substituting this value into $\angle VTW={(x+15)}^o$ , we get

  $\angle VTW={35}^o$

Now, as we know that $\overrightarrow{TV}$ bisects $\angle STW$ , we can say that

  $m\angle STW=2\angle VTW$

Thus,

  $m\angle STW={70}^0$