Question

Angle 1 is labeled 19x - 9, and angle 2 is labeled 4x + 36. If angles 1 and 2 are vertical to each other, what is the measure of angle 2?

27 degrees
81 degrees
72 degrees
36 degrees

Answer 1

To find the measure of angle 2, we set the expressions of the vertical angles equal to each other, solve for 'x', and substitute 'x' into the expression for angle 2, resulting in 48 degrees, which is not listed in the provided options.

Step-by-step explanation:

The student's question involves finding the measure of angle 2 when given two expressions for a pair of vertical angles. Vertical angles are equal in measure, so we set the expressions equal to each other and solve for 'x'. Once we have the value of 'x', we can determine the measure of angle 2 by substituting the value of 'x' into the expression for angle 2.

Let's solve for 'x':

• Set the expressions equal: 19x - 9 = 4x + 36
• Subtract 4x from both sides: 15x - 9 = 36
• Add 9 to both sides: 15x = 45
• Divide both sides by 15: x = 3

Now, substitute 'x' into the expression for angle 2:

• Angle 2 = 4x + 36
• Angle 2 = 4(3) + 36
• Angle 2 = 12 + 36
• Angle 2 = 48 degrees

Therefore, the measure of angle 2 is 48 degrees, which is not one of the options presented. The correct measure is not listed among the choices given by the student.