Answer:
1. x = 40; measure of angle is 110 deg
2. x = 37.2; the angles measure 100.6 deg and 79.4 deg
Explanation:
1.
The two angles with measures are vertical angles. Vertical angles are congruent, so their measures are equal.
3x - 10 = 2x + 30
x = 40
3x - 10 = 3(40) - 10 = 120 - 10 = 110
The measure of the angles with measures is 110 deg.
2.
The two angles form a linear pair. Angles in a linear pair are supplementary. That means that their measures add to 180 deg.
3x - 11 + 2x + 5 = 180
5x - 6 = 180
5x = 186
x = 37.2
3x - 11 = 3(37.2) - 11 = 111.6 - 11 = 100.6
2x + 5 = 2(37.2) + 5 = 79.4
The angles measure 100.6 deg and 79.4 deg