Question

1 in the diagram, line a is parallel to line b, and line t intersects lines a and b. use the diagram to fill in the blanks.
a) ( x = )

b) ( x + y = )

diagram: two parallel lines a and b, transversal t. at intersection with b: 104° and ( y^circ ); at intersection with a: ( x^circ )

Explanation:

Step1: Find x (supplementary angle)

$\text{Since } x + 104^\circ = 180^\circ, \text{ solve for } x:$
$x = 180^\circ - 104^\circ = 76^\circ$

Step2: Find y (corresponding angle)

$\text{Since } y \text{ corresponds to } x \text{ (parallel lines)},$
$y = x = 76^\circ$

Step3: Calculate x + y

$x + y = 76^\circ + 76^\circ = 152^\circ$

Answer:

a) $76$
b) $152$