7.2 Angles in Quadrilaterals

An exterior angle has a lot of important properties. They are angles opposite to the interior angles created by imaginary lines that continue to extend from the vertex. There are 2 ways to find exterior angles. The 1st way is that all the exterior angles add up to 360, NO MATTER THE SHAPE, so if all the other exterior angles are there, You can find the missing variable by adding up the 3 angles u have and subtracting that from 360. The 2nd way is if you have it’s interior angle, you can subtract that number from 180 and it will give you the answer. This is because all opposite interior and exterior angles add up to 180.

 

Example from Textbook:

 

To find x:

We know that x and "3x-33˚" will add up to 180˚. Therefore we can use the following equation:

 

3x-22+x=180

4x-22=180

4x-22+22=180+22

4x=202

4x/4=202/4

x=50.5

 

Therefore x = 50.5˚

 

To find w:

To find w we need to find all the other interior angles, we can do this by solving the equations with our x value.

 

3x-22

= 3(50.5)-22

= 151.5-22

= 129.5

 

2x-10

= 2(50.2)-10

= 101-10

= 91

 

x+15

= 50.5 +15

=65.5

 

w+129.5+91+65.5=360

w+286=360

w+286-286=360-286

w=74

 

Therefore w = 74˚

 

To find u:

We know that w+u=180˚

 

Therefore using the following equation, we can find u:

 

w+u = 180

74+u-74=180-74

u=106

 

Therefore u = 106˚

 

To find y:

We know that (2x-10)+y=180

 

Therefore using the following equation, we can find y:

 

(2x-10)+y=180

91+y=180

91-91+y=180-91

y=89

 

Therefore y = 89˚

 

(note the reason we did not do the brackets is because it is already solved for previously.)

 

 

To find z:

 

We know that (x+15)+z=180

 

Therefore using the following equation, we can find z:

 

(x+15)+z=180

65.5+z=180

65.5-65.5+z=180-65.5

z=114.5

 

Therefore z = 114.5