Can someone please help ? (:

Wow! There so much extra stuff on this drawing, naturally it's hard to see
what's going on.

First, do you remember "vertical angles" ?  They're the pair of opposite angles
that form where lines cross, and they're equal.

-- It says that angle-1 is 55 degrees.
Angle-1 and angle-7 are vertical angles, so angle-7 is also 55 degrees.

-- It says that angle-4 is 60 degrees.
Angle-4 and angle-6 are vertical angles, so angle-6 is also 60 degrees.

Now you can forget about all that stuff that's outside of the triangle in the middle,
and just look at the triangle. They want you to find angle-10.

See the angles at the top of the triangle ... angle-7 and angle-6 ?
We know what both of those are.  Angle-7 is 55 degrees, and angle-6 is 60 degrees.

Do you remember what the 3 angles inside a triangle always add up to ?
They always add up to 180 degrees.

Add angle-7 and angle-6 together . . . 55 + 60 = 115 degrees.

So angle-10 is just the rest of the 180 degrees inside the triangle.

Angle-10 = 180 - (115) = 65 degrees