Step-by-step explanation:
10.
angle QUR must be 180-41 = 139°
the reason : all angles on one side of the line QS around a single point (like U) must be 180°, as this represents a half-circle.
11.
the angle RUQ is larger.
the angle TUS is 90°.
therefore, SUN is 90° too. as well as TUQ and QUN.
the angle TUR is then TUS + 41 = 90+41 = 131°
and we know from 10. that QUR (or RUQ) is 139°.
therefore, RUQ is larger.
12.
when 2 lines cross, then the diagonally opposing angles are identical.
therefore,
84 = 4x
x = 21
13.
the same principle as in 10. applies.
all angles in one side of a line around a single point must be 180°.
so,
KMH + 84 = 180
KMH = 96°
14.
EBD = 90°
therefore, also ABE = 90°.
and we can imagine that BE extends straight to the other side of B having a point G there.
and then ABG = DBG = 90° as well.
and because these 90° angles and the principle of 12., we have
ABF = CBD = 90-62 = 28°
therefore,
CBE = CBD + DBE = 28 + 90 = 118°.
15.
ABF = 28°
as we calculated that in 14 already.
16.
due to the principles of 14 and 10 we have
CBA = 180 - CBD = 180 - 28 = 152°.
17.
this is not relevant to any of the pictures before.
angle A = angle B + 4
complementary angles are together 90°.
so,
A + B = 90
now we use the identity of the first equation in this main equation :
(B + 4) + B = 90
2B + 4 = 90
2B = 86
B = 43°
=>
A = B + 4 = 43 + 4 = 47°
18.
again, this is not related to any of the pictures before.
supplementary angles are together 180°.
D = 5E
D + E = 180
5E + E = 180
6E = 180
E = 30°
=>
D = 5E = 5×30 = 150°
