This blog post I chose to focus on finding angles with intersecting lines when it adds to 360 degrees. As well as understanding the different terms when choosing your reasonings.

reasonings:

complementary-  Angles that add to 90 degrees

supplementary- Angles that add to 180 degrees

Vertical Opposite- an equal opposite

1. The first step is I like to evaluate if It is a triangle and it adds to 360 degrees, or if it it goes all the way around and adds to 360 degrees. For this specific equation I have 104 degrees already written in for me.

2. The next step I like to take is to see how I can make a total of 360 degrees within my equation. I know that 104 + 104 = 208 which solves 2 of the angles.

3. To find the next two angels, I use the equation 360-208=152. Now that I have 152 I divide that by 2 to find the two angles that are equal. 152 divided by 2 = 76. therefor 76 is each angle.

To double check my work I use the long format to show my equation to check my answer:

104 + 104 + 76 +76 = 360

4. Now I have all my angles with all my work shown, I know can decide how to classify them with a reasoning:

For angle 5: Vertically opposite: This one I classified as vertically opposite because we are given the angle of 104 degrees on one side, and for this diagram both ends are equal. therefor, it is the same. So because it is straight across (opposites) it is vertically opp.

For angle 6: supplementary: this one I classify it as supplementary because the angle adds up to 360 degrees.

For angle 7: vertically opposite: this one I classified as vertically opposite as well, because it is right across vertically from angle 6 which is 76 degrees as well.