Answer: x = 20 and 2x + 1° = 41°
Step-by-step explanation: In this problem, we're asked to use the diagram shown to find x and then use that to find 2x + 1°.
Notice that these angles are vertical angles
so we know that the angles are congruent.
Therefore, since the measure of one angle is 7x - 99° and the measure of the other angle is 2x + 1°, we can setup the equation 7x - 99 = 2x + 1.
Solving from here, we subtract 2x from both sides to get
5x - 99 = 1 and adding 99 to both sides, we have 5x = 100.
Dividing both sides by 5, x = 20.
To find the measure of the angle 2x + 1°, we can substitute
a 20 in for x in the equation to get 2(20) + 1 or 40 + 1 which is 41.
So the measure of the angle 2x + 1° is 41°
