Question

What is the answer to these questions.

Answer 1

a) No

b)
`174^(\circ)-17x`

Explanation:

a)

If
`x=5`, we have that
`\angle c=9(5)-3=45-3=42`, and
`\angle d=8(5)+9=40+9=49`.

`42+49=91\\eq 90`, so
`\angle c` and
`\angle d` are not complementary when
`x=5`

b)

If
`\angle c`,
`\angle d`, and
`\angle e` form half a circle, that means they sum to
`180^(\circ)`.

We now need to solve
`\angle c + \angle d + \angle e = 180^(\circ)` for
`\angle e`.

Plugging in for
`\angle c` and
`\angle d` gives
`(9x-3)+(8x+9)+\angle e = 180`.

Combining like terms on the left side gives
`17x+6+\angle e = 180`.

Subtracting a
`17x` and a
`6` from both sides gives
`\angle e = 174-17x`.

This means that
`\angle e = 174^(\circ)-17x` and we're done.