Please help me find measure of x!

56

Step-by-step explanation:

angle BAD is an exterior angle of triangle ABC

angle x and angle C are opposite interior angles of exterior angle BAD

An exterior angle of a triangle is equal to the sum of its opposite interior angles

Hence angle BAD = x + angle C

we are given that angle BAD = 116 and angle C = 60

So 116 = x + 60

Notice that we just created an equation that we can use to solve for x

We now solve for x algebraically

116 = x + 60

Subtract both sides by 60

116 - 60 = 56

60 - 60 cancels out

We're left with x = 56

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).