There is a pair of vertical angles where < 1 = 106 degrees and <2 = 3x -75. What equation can you write to solve for x
Vertical angles are always congruent, which means that they have the same measure. Therefore, we can set the measure of angle 1 equal to the measure of angle 2 and solve for x.
106 = 3x - 75
To solve for x, we can add 75 to both sides of the equation:
106 + 75 = 3x
Simplifying the left side:
181 = 3x
Finally, we can divide both sides by 3 to isolate x:
x = 60.33
Therefore, the value of x that makes the vertical angles congruent is approximately 60.33 degrees.
To solve for x, we can use the fact that vertical angles are congruent. Vertical angles are formed when two lines intersect each other, and the opposite angles formed are congruent.
In this case, we are given that <1 measures 106 degrees. So, angle 1 can be represented as 106 degrees.
Angle 2 is represented as 3x - 75 degrees.
Since these angles are vertical angles, they are congruent. Therefore, we can set up an equation to solve for x:
106 degrees = 3x - 75 degrees
Now we can solve the equation for x.
To find the value of x, we can apply the property of vertical angles, which states that vertical angles are congruent. In this case, we have:
∠1 = ∠2 = 106 degrees
And also, ∠2 = 3x - 75 degrees.
Since both angles are equal to ∠2, we can set them equal to each other:
∠1 = ∠2
106 = 3x - 75
To solve for x, we will isolate the variable by performing algebraic operations:
Add 75 to each side of the equation:
106 + 75 = 3x - 75 + 75
181 = 3x
Next, divide both sides of the equation by 3:
181/3 = 3x/3
60.3333 = x
Therefore, the equation to solve for x is:
3x - 75 = 106
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75
so, 1 + 2 = 180
or, 106 + 3x - 75 = 180
3x = 180 -106 +75
3x = 149
x = 49.6
Hence, The solution is, the value is, x = 49.6.
Can someone check if my answer or the bot's answer correct?