Question

question 3. find the angle x in each question below. give reasons for your answer.
(a)
(b)
(c)
(d)
(e)
(f)

Explanation:

Step1: Identify angle - type relationship

For parallel lines cut by a transversal, corresponding angles are equal, alternate - interior angles are equal, and same - side interior angles are supplementary.

Step2: Solve for (a)

The angle of \(125^{\circ}\) and \(x\) are corresponding angles. So \(x = 125^{\circ}\)

Step3: Solve for (b)

The \(57^{\circ}\) angle and \(x\) are alternate - interior angles. So \(x=57^{\circ}\)

Step4: Solve for (c)

The \(70^{\circ}\) angle and \(x\) are corresponding angles. So \(x = 70^{\circ}\)

Step5: Solve for (d)

The \(105^{\circ}\) angle and \(x\) are corresponding angles. So \(x = 105^{\circ}\)

Step6: Solve for (e)

The \(53^{\circ}\) angle and \(x\) are same - side interior angles. Since same - side interior angles are supplementary (\(x + 53^{\circ}=180^{\circ}\)), then \(x=180^{\circ}-53^{\circ}=127^{\circ}\)

Step7: Solve for (f)

The \(133^{\circ}\) angle and \(x\) are same - side interior angles. Since same - side interior angles are supplementary (\(x + 133^{\circ}=180^{\circ}\)), then \(x = 180^{\circ}-133^{\circ}=47^{\circ}\)

Answer:

(a) \(x = 125^{\circ}\)
(b) \(x = 57^{\circ}\)
(c) \(x = 70^{\circ}\)
(d) \(x = 105^{\circ}\)
(e) \(x = 127^{\circ}\)
(f) \(x = 47^{\circ}\)