Answer:
1. 80º
2. 70º
3. 120º
4. 110º
5.90º
6.80º
7.30º
8.140º
9.40º
10. 20º
Step-by-step explanation:
The number one angle is opposite to the 80º angle that means that since they are two straight lines that are cut by one another, their opposite angles will be identical. So angle 1 is 80º.
The number two angle is opposite to the 70º angle that means that since they are two straight lines that are cut by one another, their opposite angles will be identical. So angle 2 is 70º.
The number 3 angle is suplementary to the angle that forms a right triangle with the 30º angle that means that angle 3 will be 180º-30º-90º=120º so angle 3 is 120º.
Since angle 4 is made from the cutting from a paralel line to the 70º angle is suplementary so it will be 180º-70º=110º.
Number 5 is easy cause it is a right angle so 90º.
The 6 angle is basically the same as the 4 but cut by the line that creates angle 3, so you just withdraw angle 3 from angle four to get 6= 110º-30º=80º.
The angle 7 is calculated by withdrawin angle 6 and the 70º angle from the top, since they are the same as the other angle that completes the tirangle right there, so it would be 180º-70º-80=30º.
Angle 8 is calculated using a similar technique, one angle is 10º and the other is opposite to 7, so all angles in a triangle add up to 180 so we just withdraw form 180º the other angles: 180º-10º-30º=140º
Angle 9 is suplementary on the parallel lines that cut angle 8 so we just withdraw from 180º angle 8= 180º-140º=40º
To solve angle 10, we need to create a gigantic triangle one angle being angle 1, 80º and the second being the sum of angle 2 plus the rest of the angle, since angle one creates a right triangle with the rest of the angle we calculate 80º+90º=170º-180º=10º
This means the rest of the angle is 10º. so Angle 2+10º=80º
Now we have that the two other angles that form the triangle with angle 10 add up to:
80º+80º=160º
Since all the inner angles of a triangle add up to 180, angle 10 is 20º.
