Question

In the accompanying diagram of AABC, side AB is

extended to D. If mLACB = x + 30, mL CAB = 2x + 10, and
mZCBD = 4x + 30, what is the value of x?

Answer 1

x = 10

Explanation:

The external angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠CBD is an external angle of the triangle, thus

4x + 30 = 2x + 10 + x + 30, that is

4x + 30 = 3x + 40 ( subtract 3x from both sides )

x + 30 = 40 ( subtract 30 from both sides )

x = 10