Question

I need help with a and b.

Answer 1

a) Supplementary angles.

b) The angles sum to 180°.

c) x = 66

Explanation:

According to the Corresponding Angles Theorem, when a straight line (the diagonal brace) intersects parallel straight lines (the wires), the angles in the same relative position are congruent.

If we assume that the wires are parallel, this means that the angle adjacent to the one labelled (2x + 8) is 40°. (See attachment).

These two adjacent angles form a linear pair, which means their sum is 180°. Since supplementary angles are two angles with a sum of 180°, the angle relationship represented by the two angles is supplementary.

To find the value of x, we can set up an equation where the sum of the two angles is 180°:

`(2x + 8)^(\circ) + 40^(\circ) = 180^(\circ)`

Solving for x:

`\begin{aligned}(2x + 8)^(\circ) + 40^(\circ) &= 180^(\circ)\\(2x + 8) + 40 &= 180\\2x + 8 + 40 &= 180\\2x + 48 &= 180\\2x + 48 - 48 &= 180 - 48\\2x &= 132\\2x / 2 &= 132 / 2\\x &= 66\end{aligned}`

Therefore, the value of x is 66.