STEP-BY-STEP SOLUTION:
~ Question No. 11 ~
To find x -
Corresponding angles are equivalent to each other.
There are corresponding angles in this problem. We can identify this through the 'F' shape which the angles form as well as that it is on paralell lines.
Therefore:
3x + 49 = 7x - 23
3x - 7x = - 23 - 49
- 4x = - 72
x = - 72 / - 4
x = 72 / 4
x = 18
To find y -
There are more corresponding angles in this problem. We can identify this through the 'F' shape which the angles form as well as that it is on paralell lines.
Therefore:
x = 18
3x = 11y - 1
11y - 1 = 3x
11y - 1 = 3 ( 18 )
11y - 1 = 54
11y = 54 + 1
11y = 55
y = 55 / 11
y = 5
FINAL ANSWER:
Hence, the answer is:
x = 18
y = 5
~ Question No. 12 ~
To find x -
Alternate angles are equivalent to each other.
There are alternate angles in this problem. We can identify this through the 'Z' shape which the angles form as well as that it is on paralell lines.
Therefore:
5x - 38 = 3x - 4
5x - 3x = - 4 + 38
2x = 34
x = 34 / 2
x = 17
To find y -
We will use the angle sum of a triangle to find y.
Angle sum of a triangle = 180°
Therefore:
x = 17
7y - 20 + 5x - 38 + 90 = 180
7y - 20 + 5 ( 17 ) - 38 + 90 = 180
7y = 180 + 20 - 5 ( 17 ) + 38 - 90
7y = 180 + 20 - 85 + 38 - 90
7y = 63
y = 63 / 7
y = 9
FINAL ANSWER:
Hence, the answer is:
x = 17
y = 9
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