Question

1. x =

justify:

1. y =

justify:
(there is an image of intersecting lines with angles labeled (x + 20)° and (95 - x)°)

Explanation:

Step1: Set up parallel line equation

The angles are corresponding angles for parallel lines, so they are equal:
$$x + 20 = 196 - x$$

Step2: Solve for $x$

Rearrange to isolate $x$:
$$x + x = 196 - 20$$
$$2x = 176$$
$$x = \frac{176}{2} = 88$$

Step3: Find $y$ using linear pair

$y$ and $(x+20)^\circ$ form a linear pair (supplementary):
$$y + (x + 20) = 180$$
Substitute $x=88$:
$$y + (88 + 20) = 180$$
$$y + 108 = 180$$
$$y = 180 - 108 = 72$$

Answer:

1. $x = 88$

Justify: Corresponding angles of parallel lines are equal.

1. $y = 72$

Justify: Linear pair angles are supplementary.