In the figure below, what is the value of xº ?

Around point C we have a straight line, divided into a 170 degree angle and another angle. That other angle, inside the triangle, must then be 10 degrees, because angles in a straight line sum to 180.

Triangle BCD is isosceles, so the angle at B (the one right next to 'x') must also be 10 degrees, and since the angles in a triangle sum to 180, the third angle, at point D, must be 160 degrees.

We again have a straight line passing through point D, so the two angles there must sum to 180, and we just found one of the angles was 160, so the other must be 20 degrees. Now we know the triangle ADB is isosceles, so the angles at D and A are equal, and so those must both be 20 degrees, and angle A, the third angle in that triangle, must be 140 degrees, since the three angles in a triangle sum to 180.