How can properties of linear pairs and vertical angles help determine the angle measures created by the intersecting lines?

Linear pairs are adjacent angles that are supplementary. Their measures add to 180 deg. Vertical angles are congruent. Let's say two lines intersect, and you know the measure of one of the 4 angles that were formed.

Step-by-step explanation:

it could be a ..idk tho

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).