Question

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

Explanation:

Step1: Recall corresponding - angles property

When two parallel lines are cut by a transversal, corresponding angles are equal.

Step2: Solve for (a)

Since the angle of $125^{\circ}$ and angle $x$ are corresponding angles, $x = 125^{\circ}$.

Step3: Solve for (b)

The angle of $57^{\circ}$ and angle $x$ are corresponding angles, so $x=57^{\circ}$.

Step4: Solve for (c)

The angle of $70^{\circ}$ and angle $x$ are corresponding angles, thus $x = 70^{\circ}$.

Step5: Solve for (d)

The angle of $105^{\circ}$ and angle $x$ are corresponding angles, hence $x = 105^{\circ}$.

Step6: Solve for (e)

The angle of $53^{\circ}$ and angle $x$ are corresponding angles, so $x = 53^{\circ}$.

Step7: Solve for (f)

The angle of $133^{\circ}$ and angle $x$ are corresponding angles, therefore $x = 133^{\circ}$.

Answer:

(a) $x = 125^{\circ}$
(b) $x = 57^{\circ}$
(c) $x = 70^{\circ}$
(d) $x = 105^{\circ}$
(e) $x = 53^{\circ}$
(f) $x = 133^{\circ}$