Question

question 3 (1 point)
x =
blank 1:
question 4 (1 point)
m || n
x =
blank 1:

Explanation:

Step1: Identify vertical - angle property

Vertical angles are equal. In Question 3, the angle \(x\) and the \(40^{\circ}\) angle are vertical angles. So \(x = 40\).

Step2: Identify corresponding - angle property for Question 4

Since \(m\parallel n\), the angle \(x\) and the angle \(x + 58\) are supplementary (linear - pair of angles formed by a transversal with parallel lines). So \(x+(x + 58)=180\).

Step3: Solve the equation for Question 4

\[

$$\begin{align*} x+(x + 58)&=180\\ 2x+58&=180\\ 2x&=180 - 58\\ 2x&=122\\ x&=61 \end{align*}$$

\]

Answer:

Question 3: 40
Question 4: 61