Question

the sum of two vertical angles is 140 degrees. what is the measure of one of the vertical angles?
68 degrees
138 degrees
140 degrees
70 degrees
question 7
which of the following statements is true about the following figure?
none of the angles have the same measure.
the lines that form the angles will always have the same lengths.
only alpha (α) and beta (β) have the same measure.
there are two pairs of vertical angles.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. Let the measure of each vertical angle be $x$. If the sum of two vertical angles is 140 degrees, then $x + x=140$.

Step2: Solve the equation

Combining like - terms gives $2x = 140$. Dividing both sides by 2, we get $x=\frac{140}{2}=70$ degrees.

For the second question:

Step1: Identify vertical angles

When two lines intersect, vertical angles are formed. In the given figure where two lines intersect, $\alpha$ and $\beta$ are one pair of vertical angles and $\gamma$ and $\delta$ are another pair of vertical angles. So, there are two pairs of vertical angles. Lines forming angles are rays (extend infinitely) and don't have a fixed length, and vertical angles are equal in measure, not just $\alpha$ and $\beta$.

Answer:

1. D. 70 degrees
2. D. There are two pairs of vertical angles.