Question

what is the value of r?

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. The angle opposite to \(64^{\circ}\) is also \(64^{\circ}\).

Step2: Apply angle - sum relationship

We know that \(r + 25^{\circ}=64^{\circ}\) (because the sum of \(r\) and \(25^{\circ}\) makes an angle equal to the vertical - angle of \(64^{\circ}\)).

Step3: Solve for \(r\)

Subtract \(25^{\circ}\) from both sides of the equation \(r + 25^{\circ}=64^{\circ}\). So, \(r=64^{\circ}-25^{\circ}\).

Answer:

\(39\)