Question

ZA and B are vertical angles. If mZA = (3x + 13) and mZB = (5x + 9)°,

then find the measure of ZA.

Answer 1

To find the measure of angle ZA, equate the expressions for vertical angles ZA and ZB, solve the resulting equation for x, and substitute the value of x back into the expression for ZA to get a measure of 19 degrees.

Step-by-step explanation:

The student is asking about vertical angles, which are equal when two lines intersect each other. Specifically, we are given that the measure of angle ZA is represented by the expression (3x + 13) degrees and the measure of angle ZB is (5x + 9) degrees. Since ZA and ZB are vertical angles, their measures must be equal. To find the measure of ZA, set the two expressions equal to each other and solve for x.

Steps to Solve

1. Set the expressions equal: (3x + 13) = (5x + 9)
2. Solve for x by subtracting 3x from both sides: 13 = 2x + 9
3. Subtract 9 from both sides: 4 = 2x
4. Divide both sides by 2 to get x = 2
5. Plug x back into the expression for ZA to find the measure: mZA = 3(2) + 13
6. Calculate mZA: mZA = 6 + 13 = 19 degrees

Therefore, the measure of ZA is 19 degrees.