Answer:
1 ) x = y = 9
2 ) x = 5, y = 25
3 ) x = 15, y = 9
4 x = 30, y = 15
Explanation:
1 )
The shape is parallelogram.
In parallelogram, alternate interior angles are equal.
9x and 45 are alternate interior angles.
So,
9x = 45
Divide 9 on both sides,
x = 45 / 9
x = 5
In square, opposite side lengths are equal.
2y = 18
Divide 2 on both sides,
y = 18 / 2
y = 9
2 )
The shape is parallelogram.
In parallelogram, the sum of adjacent angles are 180.
In parallelogram, opposite angles are equal.
5y and 55 are adjacent angles,
5y + 55 = 180
5y = 180 - 55
5y = 125
Divide 5 on both sides,
y = 125 / 5
y = 25
11x and 55 are opposite angles,
11x = 55
Divide 11 on both sides,
x = 55 / 11
x = 5
3 )
The shape is parallelogram.
In parallelogram, alternate interior angles are equal.
2x and 30 are alternate interior angles,
2x = 30
Divide 2 on both sides,
x = 30 / 2
x = 15
x + y and 24 are also alternate interior angles,
x + y = 24
15 + y = 24
y = 24 - 15
y = 9
4 )
The shape is a square.
Square is also a parallelogram.
All the four angles in a square are 90 and are equal.
So,
3x = 90
Divide, 3 on both sides,
x = 90 / 3
x = 60
6y = 90
Divide 6 on both sides,
y = 90 / 6
y = 15