Question

1. what is the value of x? 10 points a) x = 10 b) x = 9 c) x = 6 d) x = 4 13) if two angles forming a linear - pair are supplementary, then they can never be congruent at the same time. true or false? 10 points 14) solve for x then find the value of each of these angles and provide the name of the angle pair. 10 points x = __ angles measure = and name of angle pair: __

Explanation:

Step1: Solve for x in question (2)

Set the two expressions equal:
\[20x + 5=24x - 1\]
\[24x-20x=5 + 1\]
\[4x=6\]
\[x=\frac{6}{4}=1.5\]
However, this value is not in the given options. There might be a misunderstanding in the problem - assuming the two - line segments are equal in length and setting up the equation as above.

Step2: Answer question (13)

Two angles in a linear - pair are supplementary (sum to 180°). They can be congruent when each angle is 90°. So the statement "If two angles forming a linear pair are supplementary, then they can never be congruent at the same time" is False.

Step3: Solve for x in question (14)

If the two angles are vertical angles (assuming they are vertical angles as they are opposite each other in the intersection of two lines), then they are congruent.
Set \((8x + 17)=(5x+19)\)
\[8x-5x=19 - 17\]
\[3x=2\]
\[x=\frac{2}{3}\]
The measure of the first angle: \(8x + 17=8\times\frac{2}{3}+17=\frac{16}{3}+17=\frac{16 + 51}{3}=\frac{67}{3}\approx22.33^{\circ}\)
The measure of the second angle: \(5x + 19=5\times\frac{2}{3}+19=\frac{10}{3}+19=\frac{10+57}{3}=\frac{67}{3}\approx22.33^{\circ}\)
The name of the angle - pair is vertical angles.

Answer:

(2) None of the above
(13) False
(14) \(x = \frac{2}{3}\), Angles measure=\(\frac{67}{3}\) and \(\frac{67}{3}\), Name of angle pair: Vertical angles