Question

Determine the value of x in the diagram below.

Answer 1

AD=BD=CD
<BAC = 60°
<ABC = 70°

Answer 2

assuming thats a regular tetrahedron < BAC = 60 degrees

Answer 3

each face is an equilateral triangle

Answer 4

I'm first going to add some more labels to your diagram. This will make things considerably easier. Plus, we know we have pairs of x, y, and z because we have 3 isosceles triangles with ADB, BDC, and CDA. That's the groundwork. Now the solution next.

Answer 5

z = 70 - y Also, z = 50 -x So, 70 - y = 50 - x

We also know that x + y = 60 so we now have 2 simultaneous equations in variables x and y.

Solving, we have:
y - x = 20 and y + x = 60

Adding these two equations, we have 2y = 80 or y = 40
So, x = 20

Incidentally, z = 30

Answer 6

Nice solution. This question makes a lot more sense now. Thanks for the help

Answer 7

This was a tricky but immensely fun problem And you're welcome!