I'll do part (a) to get you started.
The angle 'a' pairs up with the 123 degree angle as a corresponding angle pair. Due to the parallel lines, the corresponding angles are congruent. Therefore a = 123.
We also see that b = 123 as well since a = b (they are vertical angles).
Notice how angle c is adjacent to the 123 degree angle. These two angles form a straight line, so they must add to 180 degrees.
c+123 = 180
c = 180-123
c = 57
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To summarize, we have these three angles
a = 123
b = 123
c = 57
Rewrite the equations;
m+4n=8
m-n=-2
Eliminating m gives;
5n=10
n=2
Replacing for n in the first equation;
m+4(2)=8
m=8
Answer;
(0, 2)
Answer:
AX : XB as AB : AC
AX = 5
XB = 4
AC = 6
AB = x
Step-by-step explanation:
5 : 4 as to x : 6
ratios can also be written as fractions...
5/4 = x/6 ..now we have a proportion...so we cross multiply
(4)(x) = (5)(6)
4x = 30
x = 30/4
x = 15/2 <==== AB = 15/2
Because of exterior angles theorem, y=39+65, so y=104
x and y are a linear pair, so they add up to 180. x=180-104, x=76
all angles in a triangle add up to 180, so 21+104+z=180. therefore, z=55
y=104
x=76
z=55
