Question

1. for each of the following, state the relationship between the two angles shown and find the value of x.

a) b) c)

Explanation:

Step1: Identify angle - relationship in a)

The two angles are corresponding angles. Corresponding angles formed by parallel lines and a transversal are equal.
$x = 142$

Step2: Identify angle - relationship in b)

The two angles are alternate - interior angles. Alternate - interior angles formed by parallel lines and a transversal are equal.
$x = 115$

Step3: Identify angle - relationship in c)

The two angles are same - side interior angles. Same - side interior angles formed by parallel lines and a transversal are supplementary (sum to 180°).
$x=180 - 95$
$x = 85$

Answer:

a) Relationship: Corresponding angles, $x = 142$
b) Relationship: Alternate - interior angles, $x = 115$
c) Relationship: Same - side interior angles, $x = 85$