Find x and y for question 4, find x, y, and z for question 6

Start by finding x. Look at the second parallel line; you have a straight line that is made up of a 90 degree angle, 2x, and x.

Since a straight line is 180 degrees, and you know a part of it is already 90 degrees, you can make 2x and x add up to 90 degrees.

2x + x = 90, combine like terms.

3x = 90, divide both sides by 3.

x = 30

Find y next. 2y and x are on opposite sides of the transversal and make a Z shape, so they must be alternate interior angles. The alternate interior angle theorem states that these types of angles are congruent.

We know what x is, 30 degrees, so make 2y and x equal to each other.

2y = 30, divide both sides by 2.

y = 15

Find z. Same thing as the bottom parallel line; 2y and z make up the straight line so they must add up to 180 degrees. We found y was 15, so multiply y by 2. y = 30, so make 30 + z add up to 180 degrees.

30 + z = 180, subtract 30 from both sides.

x = 150

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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