Question

Please help thank you very much and show all work

Answer 1

Question 1:

Angle D and angle E are congruent because they are alternate interior angles. Let's make an equation.

$5(x-2)=x+14$

Use the distributive property

$5x-10=x+14$

Add both sides by 10 and subtract both sides by x

$4x=24$
$x=6$

Plus this in and you get 20 for both of them (they're supposed to be congruent).

Your answer is the first choice.

Question 2:

Use the sine. The sine is the opposite leg divided by the hypotenuse. Divide the sine from 400 to get our answer.

$\dfrac {400}{sin(7)} \approx 3282$

Your answer is the third choice.

Question 3:

Use the tangent. The tangent is the opposite side divided by the adjacent. Divide 203 by the tangent of 22 degrees.

$\dfrac{203}{\tan(22)} \approx 502.4$

Your answer is the third choice. I hope this helps! :)