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.

Answer 1

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°.