Question

1 determine the measure of all the angles. a

Explanation:

Step1: Identify angle - relationship

The angles \(x^{\circ}\) and \(4x^{\circ}\) are same - side interior angles. For parallel lines, same - side interior angles are supplementary, so \(x + 4x=180\).

Step2: Solve the equation

Combining like terms, we get \(5x = 180\). Then, dividing both sides by 5, \(x=\frac{180}{5}=36\).

Step3: Find angle measures

The first angle is \(x = 36^{\circ}\). The second angle is \(4x=4\times36 = 144^{\circ}\). Corresponding angles to these will have the same measures, and vertical angles to these will also have the same measures.

Answer:

The angles are \(36^{\circ}\) and \(144^{\circ}\), and the angles with the same measures as their corresponding and vertical angles are also \(36^{\circ}\) and \(144^{\circ}\) respectively.