What are the measures of the marked angles?
The figure shows a horizontal line cut by another line. The angle formed above the horizontal line and to the left of the intersection point is labeled as 3 x minus 8 degrees. The angle formed below the horizontal line and to the right of the intersection point is labeled as 2 x plus 1 degree.
A.
19
°
B.
27
°
C.
38
°
D.
90
°
Since the two lines form an "X" shape, the opposite angles are congruent. Therefore, we have:
3x - 8 = 2x + 1
Solving for x, we get:
x = 9
Substituting back into the given expressions, we get:
3x - 8 = 3(9) - 8 = 19 degrees
2x + 1 = 2(9) + 1 = 19 degrees
Therefore, the measures of the marked angles are both 19 degrees (option A).
To find the measures of the marked angles, we can set up an equation and solve for the variables.
The angle above the horizontal line and to the left of the intersection point is labeled as 3x - 8 degrees.
The angle below the horizontal line and to the right of the intersection point is labeled as 2x + 1 degree.
Since they are vertically opposite angles, they are equal to each other.
So, we have the equation:
3x - 8 = 2x + 1
To solve the equation, we can subtract 2x from both sides:
3x - 2x - 8 = 1
Simplifying, we get:
x - 8 = 1
Next, we can add 8 to both sides:
x - 8 + 8 = 1 + 8
x = 9
Now that we have found the value of x, we can substitute it back into one of the equations to find the measure of either angle.
Using the equation for the angle above the horizontal line and to the left of the intersection point:
3x - 8 = 3(9) - 8 = 27 - 8 = 19 degrees
Therefore, the measure of the angle above the horizontal line and to the left of the intersection point is 19 degrees.
Answer choice A: 19 °
To find the measures of the marked angles, we need to set up an equation based on the given angles and solve for the variable, x.
The angle above the horizontal line and to the left of the intersection point is labeled as "3x-8 degrees."
The angle below the horizontal line and to the right of the intersection point is labeled as "2x+1 degrees."
Since the two angles are vertical angles (opposite angles formed by intersecting lines), they have equal measures.
Therefore, we can set up the equation: 3x - 8 = 2x + 1.
Now, let's solve this equation to find the value of x.
Rearranging the equation, we have: 3x - 2x = 1 + 8.
Simplifying, we get: x = 9.
To find the measures of the marked angles, substitute the value of x back into the given expressions:
The angle above the horizontal line and to the left of the intersection point: 3(9) - 8 = 27 degrees.
The angle below the horizontal line and to the right of the intersection point: 2(9) + 1 = 19 degrees.
Therefore, the measures of the marked angles are:
A. 19 degrees