Question

angle 1 and angle 2 are vertical angles. If angle 1 = (5x + 12)° and angle 2 = (6x - 11), find angle 1.

Answer 1

Vertical angles are angles that are oposed by their vertex. When this happens their numerical value is equal, therefore to find the value of the angles we need to make them equal and solve the expression for the "x" variable.

`\begin{gathered} \text{angle}1\text{ = angle2} \\ 5x\text{ + 12 = 6x - 11} \\ 5x\text{ - 6x = -11 -12} \\ -x\text{ = -23} \\ x\text{ = 23} \end{gathered}`

We need to calculate the value of "angle 1", which obeys the following expression:

`\text{angle 1 = 5x + 12}`

Since x = 23, we have:

`\begin{gathered} \text{angle 1 = 5}\cdot23\text{ + 12} \\ \text{angle 1 = }115+12 \\ \text{angle 1 = 127} \end{gathered}`

The value of angle 1 is 127 degrees.