Answer:
4. Equation: 2x + x = 141
x = 47
Bigger angle measure: 94 degrees
Smaller angle measure: 47 degrees
5. Equation: 3x = 20
x = 20/3
Both of the angles have a measure of 20 degrees
Explanation:
Hey there!
Before solving #3 we need to know some basic angle facts:
If a ray splits an angle, then the two angles that are formed always add up to the original angle
In this case, 141 degrees get split up by a ray forming two new angles:
2x and x
This means that 2x and x added together will equation 141 giving us the equation:
2x + x = 141
Now, all we do is simplify and substitute the answer into the angles:
3x = 141
x = 47
2(47) = 94
1(47) = 47
Now onto #4!
For this question, there is an angle theorem that you must know in order to answer this question with ease:
Vertical angle theorem
This states that any two angles that are formed by two intersecting lines and are opposite will always be the same
With this information, we can form the following equation:
3x = 20
Now we simplify and substitute again:
3x = 20
x = 20/3
Since the angle opposite to 3x is 20 degrees, we can use the vertical angle theorem and come to a conclusion that the angle 3x has a value of 20
Hope this helped! If you have any questions or doubts, please feel free to tell me in the comments section below! Have a great rest of your day!