Question

What is the answer to these questions.

Answer 1

Answer:

a) No

b) $174^{\circ}-17x$

Step-by-step explanation:

a)

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

$42+49=91\neq 90$, 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.