Question

Find the value of x in the problem. show work. help please

Answer 1

Answer:

Step-by-step explanation:

Because of the isosceles triangle theorem, in the triangle on the left, the topo angle and the base angle on the right are congruent. That base angle is congruent to the upper left angle in the triangle on the right (the one that's upside down) because they are vertical and vertical angles are congruent. Tis upside down triangle also is isosceles, so that angle that is vertical is congruent to the angle that is vertical to x. So let's find out what that is because the angle that is vertical to x is equal to x (and 2 out of the 3 angles in both traingles!) Go back to the triangle on the left. The exterior angle there is 120, and that makes it supplementary to the right next to it on the insde of the triangle. 180 - 120 = 60. And by the Triangle Angle-Sum Theorem, knowing that the other 2 angles are congruent, 180 - 60 = 120 and 120 divided in half makes those other 2 angles 60 as well. That means that the angle vertical to x is 60 and x = 60 as well. Both of these triangles are equilateral and equiangular.