Question

helper will get a medal!!!

Answer 1

@satellite73 help?

Answer 2

A ver important property of the triangle is:
that the sum of the internal angles add up to 180º, at least in the classic geometry.
So, looking at the angles, we have a variable, and we are asked for it's value. Very well.
Let's first begin by finding all those angles, we have two, but the third, not quite.
We need to know the angle TSU before using the property of the triangles.
but there is a line defined, the line UC that contains S.
So, that must mean that angle CST and angle TSU must add up to 180º.
so by that:
\[<CST+<TSU=180º\]
but CST is 115º, so therefore:
\[115º+<TSU=180º\]
\[<TSU=180º-115º=65º\]
\[<TSU=65º\]
So, now that we have all the internal angles, let's apply the property of the triangle I stated earlier, the sum of all angles, must add up to 180º.
\[<TSU+<STU+<TUS=180º\]
So, replacing their value:
\[65+(10x)+(9x+1)=180\]
All you have to do now is find "x" :)

Answer 3

there is another important property

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

so this means

115 = 10x + 9x + 1

or

115 = 19x + 1

noe solve for x