In the figure below, not drawn to scale, ACD is a straight line and ABC is an isosceles triangle. If BCD equal 78° find X.
Since ABC is an isosceles triangle, we know that angles BAC and BCA are equal. Let's denote each of these angles as ∠BAC = ∠BCA = y.
Since the sum of angles in a triangle is 180°, we can write an equation for angle B as follows:
y + y + 78 = 180
2y + 78 = 180
2y = 102
y = 51
Now, since ∠BAC and ∠BCA are equal, we know that ∠BCA = 51° and ∠BCD = 78°.
Therefore, angle X can be calculated as follows:
X = ∠BCA + ∠BCD
X = 51° + 78°
X = 129°
So, angle X is equal to 129°.