1 Answer

Electric Monk · Answer 1 · 2022-07-13T09:18:08+0000

Answer:

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
from both sides gives
$\angle e = 174-17x$ .

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

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