Question

Help the pic has questions

Answer 1

a)
`x = 9`

b)
`m \angle 1 = m \angle 2 = 54^\circ`

Explanation:

Since
`r\ ||\ s`, through the Alternate Angle Theorem,
`m \angle 1 = m \angle 2`. We can solve for x by setting up an equation where both angles are equal to each other:

`m \angle 1 = m \angle 2\\63-x = 72-2x\\63 +x = 72\\x = 9`

Now plug in x for both of the formulas to get their angles:

`m \angle 1 = (63 - x)^\circ = (63-9)^\circ = 54^\circ`
`m \angle 2 = (72-2x)^\circ = (72-2(9))^\circ = (72-18)^\circ = 54^\circ`