Answer:
The sum of the inner angles of a triangle is 180°.
For 1) it's 180-78 = 102, decided by 2, solution is 51°
For 2) it's the same, just with a rotated image,
180-86 = 94, decided by two (for two corners), gives 48°
3) is tricky. We know that H & J got the same angle, because we see the markings on the lines.
so 8x = 6 x + 18
because they are equal
that gives 2 x = 18, or x = 9
H was 8x, so it's 72°
4) works like 3)
I look into 5 and 6 but press send for now to get the answers saved and out asap ;)
edit)
4) 2x = x + 30
subtract 1x on each side
x = 30
M is 30 + x, so it's 60°
(like all angles of this triangle btw)
5) is complicated, but I'll try to break it down.
Let's focus on the left triangle for a moment.
The upper corner got an angle of 90°-62° = 28°. That's because it's a right angle and 62° is the same angle we find further right.
The lower corner also has to have an angle of 28°, so 56° is the sum of both.
180°-56° is 124° for the right corner of the triangle we focus on.
x has to be -8 to satisfy the given equation.
6) give me another minute
edit:
for now, I can't solve 6) right away. But I'll keep thinking about the problem.
edit:
6) nasty one...
Okay, because the marked linked are of equal length, we can say that the lower triangle got also 69° in the lower corner and an angle of 42° in the left corner (180-69-69)
This leases 48° of the right angle for the upper triangle, same corner.
The marked lines here are also of same length, so the upper angle is also 48°
We can ignore the 3rd angle of the upper triangle, even though we could calculate it.
2 is 48, and it's x + 139
so
48 = x + 139
subtract 139 on both sides
-91 = x
The value of x is -91
You are welcome
