Hello there. To solve this question, we'll have to remember some properties about angles relationships.
1. This is a shallow angle, that is, an angle that measures 180º.
To find the value of x, we make:
14x + 20º + 6x = 20xº + 20º = 180º
Divide both sides of the equation by a factor of 20º
x + 1 = 9
Subtract 1 on both sides
x = 8
To find the measure of the angle TOU, plug in x into 14x + 20:
14 * 8 + 20 = 112 + 20 = 132º
2. This is a right angle, that is, their sum is equal to 90º.
To find x, you make:
12xº + (10x - 18)º = 90º
22xº - 18º = 90º
22xº = 108º
x = 108/22 = 54/11.
To find the measure of the angle OMN, plug in x into (10x - 18)º
(10 * 54/11 - 18)º
(342/11)º approx 31.1º
3. This is a vertically opposite angles case, where the angles AEB and DEC are equal to each other. Therefore we have:
(16x + 12)º = (18x - 4)º
2xº = 16º
x = 8
Plugging in this value in any of the expressions would suffice, but we will plung into the expression for AEB = BEA
16 * 8 + 12 = 128 + 12 = 140º