In geometric figure two intersecting lines creating four angles. If <1 and <3 are a vertical pair <1= 4x + 26 degrees and <3 = 98 degrees what is the value of x
Vertical angles are always equal, which means that <1 = <3. Therefore, we can set the two expressions equal to each other and solve for x:
4x + 26 = 98
Subtracting 26 from both sides, we get:
4x = 72
Dividing both sides by 4, we get:
x = 18
Therefore, the value of x is 18 degrees.
To find the value of x in this problem, we can start by using the information given about vertical angles.
Vertical angles are formed when two lines intersect. They are opposite to each other and have equal measures. In this case, angles <1 and <3 are vertical angles, so they are equal.
We are given that <1 = 4x + 26 degrees and <3 = 98 degrees. Since <1 and <3 are equal (vertical angles), we can set up an equation and solve for x.
4x + 26 = 98
To solve this equation for x, we need to isolate the variable on one side of the equation.
Subtract 26 from both sides:
4x + 26 - 26 = 98 - 26
4x = 72
Divide both sides by 4 to solve for x:
4x/4 = 72/4
x = 18
Therefore, the value of x is 18.
To find the value of x, we can use the properties of vertical angles. Vertical angles are congruent, which means they have equal measures.
We know that <1 and <3 are a vertical pair, and their measures are given as <1 = 4x + 26 degrees and <3 = 98 degrees.
Since vertical angles are congruent, we can set up an equation:
<1 = <3
Substituting the given measures, we have:
4x + 26 = 98
To solve for x, we need to isolate the variable. Let's begin by subtracting 26 from both sides:
4x = 98 - 26
4x = 72
Now, divide both sides by 4 to solve for x:
x = 72/4
x = 18
Therefore, the value of x is 18.