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P = 120 degrees, Q = 90 degrees

Step-by-step explanation:

The sum of exterior angles in a polygon is always equal to 360 degrees.

So, 9z + 5z + 10z + 12z = 360

36z = 360

z = 10

so P = 12z, since they are vertical angles they are equal, P = 120 degrees

Q is a linear pair with 9z, so 9(10)= 90 and 180-90= 90 so Q = 90 degrees

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).

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: