in the diagram shown in the comments, two lines intersect to form four angles. the measures of the angles are given in terms of the variables a,b,c and d. find the value of a.

Question

anonymous · Answer

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anonymous · Answer

Well, we know that vertical angles are congruent, so 4a = 2b+6 and 12b+6 = 8c+5d. Also, 4a + (12b+6) = 180 and (2b+6) + (8c+5d) = 180.

anonymous · Answer

Let's go with (12b+6) + (2b+6) = 180. Solve it...

14b + 12 = 180
14b = 168
168/14b = 12
b = 12

Do you know what to do from there?

anonymous · Answer

Hint: Remember that (2b+6) = 4a? So all you have to do is substitute 12 for b and you can solve for a.

anonymous · Answer

2(12) + 6 = 4a
30 = 4a
30/4a = 7.5
a = 7.5