Answer:
This is a doozy so hang on
Explanation:
I assume you want me to start from 1 so I'll make this short n' sweet
1: angle 1 = 87° by the alternate interior angle theorem and angle 2 can be found by subtracting 87 from 180 also known as the supplementary angles theorem. 180 - 87 = 93° | 1 = 87° 2 = 93° |
2: angle 1 is 78° by the congruent supplements theorem. Angle 2 is also 78° by the vertical angles theorem
3: like 2: angle 1 is 41° by the congruent supplements theorem. Angle 2 is also 41° by the vertical angles theorem
4: the same thing is 124° because of (CST) and angle 2 is 124° because of vertical angles.
5: a bit trickier, we know 37° is the same as (6x -11) due to the Supplementary theorem
So write your equation as (6x - 11) = 37
Add 11 To both sides + 11 + 11
6x = 48 dived both sides by 6
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6
X = 8
Since it only asks you for X there is no need to solve it.
6: same thing 2( x + 9) = 2. We know that equals 2 by doing the vertical angle theorem and then the supplementary angle theorem.
Solving for that you get -8 for x
7: ⅔(x +27) = (3x - 25) again...we know they are equal due to vertical angles and (CST).
Solving you get 129/7 or 18.42 as x
8: using vertical angles then alternate interior angles theorem (3x - 8) = ( x + 24) x = 16
9: 1 is = 112 by vertical angles theorem 2 = 68 by the supplementary theorem that's due to 3 = 112 by alt interior angles theorem
10: 1 = 45 by alt and 2 = 135 by sup and 3 = 135 by alt
Finished hoped this helps.