In a geographic figure to intersecting lines create four angles if angle 1 and 3 are a vertical pair one is 4x + 26 and angle 3 is 98 degrees what is the value of x
Since angles 1 and 3 are a vertical pair, they are congruent (meaning they have the same measure). We know that angle 3 is 98 degrees. Therefore, angle 1 must also be 98 degrees.
To find the value of x, let's look at angle 4. Angle 4 and angle 1 are alternate exterior angles, meaning they are congruent. We are given that angle 4 is 4x + 26 degrees.
Since angle 1 is 98 degrees, we can set up an equation:
4x + 26 = 98
Subtracting 26 from both sides:
4x = 98 - 26
4x = 72
Finally, we divide both sides by 4 to solve for x:
x = 72/4
x = 18
So, the value of x is 18.