Find angle A if angle A is supplementary to angle B, angle B is supplementary to angle C, angle B equals 12x plus 8, and angle C equals 8x minus 8
i am confusion
so clearly
A+B = 180
B+C = 180
subtract them
A - C = 0
A = C
given: B = 12x+8 , C = 8x - 8
in B+C=180
12x+8 + 8x-8 = 180
20x = 180
x = 9
so C = 72-8 = 64
but A = C
so A = 64
check:
A = 64°
B = 116°
C = 64°
is A+ B = 64+116 = 180 ? YES
is B+C = 116+64 = 180° yes
is A = C ? yes
Well, well, well, it looks like we have a chain of angles here! Let's follow the angle trail and find angle A.
Given that angle A is supplementary to angle B, we know that angle A + angle B = 180 degrees.
And since angle B is supplementary to angle C, we have angle B + angle C = 180 degrees as well.
Now, we can substitute the expressions we have for angles B and C:
12x + 8 + 8x - 8 = 180
Combine like terms:
20x = 180
Divide both sides by 20:
x = 9
Fantastic! We've found the value of x. Now, let's substitute it back into angle B to figure that out:
angle B = 12(9) + 8
angle B = 108 + 8
angle B = 116 degrees
Finally, we can find angle A since we know that angle A + angle B = 180 degrees:
angle A + 116 = 180
Subtract 116 from both sides:
angle A = 64 degrees
There you have it! Angle A is 64 degrees.
Angle a supplementary Angle b ,Angle a supplementary Angle c , then angle b and angle c are
To find angle A, we need to use the information given to us.
First, we know that angle A is supplementary to angle B. This means that the sum of angle A and angle B is 180 degrees.
So, we can write the equation: Angle A + Angle B = 180.
Next, we are given that angle B is supplementary to angle C. Again, this means that the sum of angle B and angle C is 180 degrees.
So, we can write the equation: Angle B + Angle C = 180.
We are given that angle B equals 12x + 8, and angle C equals 8x - 8.
Now, we can substitute these values into the equation:
(12x + 8) + (8x - 8) = 180.
Simplifying this equation, we have:
12x + 8 + 8x - 8 = 180.
Combining like terms, we get:
20x = 180.
Dividing both sides by 20, we find:
x = 9.
Now, we can substitute the value of x back into the expressions for angle B and angle C:
Angle B = 12x + 8 = 12(9) + 8 = 108 + 8 = 116 degrees.
Angle C = 8x - 8 = 8(9) - 8 = 72 - 8 = 64 degrees.
Finally, we can substitute the values of angle B and angle C into the equation Angle A + Angle B = 180:
Angle A + 116 = 180.
Subtracting 116 from both sides:
Angle A = 180 - 116 = 64 degrees.
Therefore, angle A is 64 degrees.