Question

two lines intersect at point p. if the measures of a pair of vertical angles are (2x - 7)° and (x + 13)°, determine x and the measures of the other two angles?

Explanation:

Step1: Set vertical - angles equal

Since vertical angles are equal, we set up the equation $2x - 7=x + 13$.

Step2: Solve for x

Subtract $x$ from both sides: $2x-x-7=x - x+13$, which simplifies to $x-7 = 13$. Then add 7 to both sides: $x=13 + 7$, so $x = 20$.

Step3: Find the measure of the given vertical - angles

Substitute $x = 20$ into either of the angle expressions. Using $2x-7$, we get $2\times20-7=40 - 7=33^{\circ}$.

Step4: Find the measure of the other two angles

The other two angles are supplementary to the given vertical - angles. Let the measure of one of the other angles be $y$. Then $y+33^{\circ}=180^{\circ}$, so $y = 180^{\circ}-33^{\circ}=147^{\circ}$.

Answer:

$x = 20$, the measures of the other two angles are $147^{\circ}$ each.