a) 12 degrees
b) 15 degrees
c) 140 degrees
d) 22 degrees
Step-by-step explanation:
Step 1 :
a)
The angles in a straight line sup to 180 degrees
So we have
10 x - 20 + 6 x + 8 = 180
16 x - 12 = 180 => 16 x = 192 => x = 192/16 = 12
Hence the value of x is 12
Step 2 :
b)
Given angles 1 and 2 are complementary which implies that their sum is 90 degrees
so we have, x + 3 x + 30 = 90
=> 4x + 30 = 90 => 4x = 60 => x = 15
Hence x has a value of 15 degrees
Step 3 :
c)
Given that the sum of the angles inside the figure is 720 degrees.
So we have,
x - 60 + x - 40 + x - 20 + 130 + 120 + 110 = 720
3x +240 = 720 +> x = 160
measure of angle F is x - 20 = 160 - 20 = 140 degrees
Step 4 :
d)
We know that the triangles 3 angles sum is 180 degrees.
So we have,
x + 120 + x + 160 = 180 => 2x = 44 => x =22
So angle B measures 22 degrees