The final Answere is Angles B & C: 41.5°, Angle D: 95°.
∆BCD is isosceles (BC = BD), the measures of ∠B and ∠C are equal. We can let x represent the measure of each of these angles.
We are given that the measure of ∠D = 2x + 14°.
The sum of the measures of the angles in a triangle is 180°, so we can write the equation:
x + x + (2x + 14°) = 180°
Combining like terms, we get:
4x + 14° = 180°
Subtracting 14° from both sides, we get:
4x = 166°
Dividing both sides by 4, we get:
x = 41.5°
Therefore, the measure of ∠B and ∠C is 41.5° each, and the measure of ∠D is 2(41.5°) + 14° = 95°.
So the answer is:
x = 41.5°
∠B = 41.5°
∠C = 41.5°
∠D = 95°
I hope this helps! Let me know if you have any other questions.