Question

1. what is the value of x? 15. find the slope of the line. 16. find the slope of the line that passes through (17, 2) and (17, - 3)

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $114^{\circ}=x + 2x$.

Step2: Combine like terms

Combining the terms on the right - hand side gives $114^{\circ}=3x$.

Step3: Solve for x

Dividing both sides by 3, we get $x=\frac{114}{3}=38$.

Step4: For question 15

The line is a vertical line. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a vertical line, $x_1=x_2$. In the given vertical line, the change in x ($\Delta x$) is 0. Since division by 0 is undefined, the slope of a vertical line is undefined.

Step5: For question 16

Let $(x_1,y_1)=(17,2)$ and $(x_2,y_2)=(17, - 3)$. Using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-3 - 2}{17 - 17}=\frac{-5}{0}$, which is undefined.

Answer:

1. $x = 38$
2. Undefined
3. Undefined