Find the value of x in each case:

You can set up an equation for the large triangle made up of the smaller ones by knowing that the total interior angles must sum to 180°. We also can know that angle RPN is also 78° by the geometric law of alternate interior angles. Therefore you know that the angles to sum up are 2x, 2x (which comes from x + x), and 78°.

2x + 2x + 78 = 180

4x + 78 = 180

4x = 102

x = 25.5°

*note, there are many ways to solve this

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it