Answer:
see explanation
Step-by-step explanation:
(35)
(9x - 4) and (8x + 7) are vertically opposite and are congruent , then
9x - 4 = 8x + 7 ( subtract 8x from both sides )
x - 4 = 7 ( add 4 to both sides )
x = 11
Then
8x + 7 = 8(11) + 7 = 88 + 7 = 95
(7y - 34) and 95 are adjacent angles on a straight line and sum to 180° , so
7y - 34 + 95 = 180
7y + 61 = 180 ( subtract 61 from both sides )
7y = 119 ( divide both sides by 7 )
y = 17
(36)
(7y - 9) and (5y + 5) are vertically opposite and are congruent , then
7y - 9 = 5y + 5 ( subtract 5y from both sides )
2y - 9 = 5 ( add 9 to both sides )
2y = 14 ( divide both sides by 2 )
y = 7
Then
5y + 5 = 5(7) + 5 = 35 + 5 = 40
(6x + 50) and 40 are adjacent angles on a straight line and sum to 180°
6x + 50 + 40 = 180
6x + 90 = 180 ( subtract 90 from both sides )
6x = 90 ( divide both sides by 6 )
x = 15
Step-by-step explanation:
35.
the angles with x must be equal.
this is just a basic attribute of crossing lines. the crossing angles above and below a picked line are simply the same (just mirrored).
so,
8x + 7 = 9x - 4
11 = x
the angle with y is a complementary angle to either angle with x, as the sum of all angles in one side of a line is 180 degrees. let's pick 8x + 7
so,
7y - 34 + 8x + 7 = 180
7y - 34 + 8×11 + 7 = 180
7y + 61 = 180
7y = 119
y = 17
36.
similar here. just here the y angles are equal, and the x angle is complementary.
5y + 5 = 7y - 9
14 = 2y
y = 7
6x + 50 + 5y + 5 = 180
6x + 50 + 5×7 + 5 = 180
6x + 90 = 180
6x = 90
x = 15