Final answer:
By applying the exterior angle theorem to the given angles in Δbcd, we determine the value of x to be 14.
Step-by-step explanation:
To find the value of x in Δbcd where the line segment bd is extended through point d to point e, we can use the properties of exterior angles in a triangle. The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.
Given:
m∠bcd = (3x + 11)°
m∠dbc = (2x + 16)°
m∠cde = (8x - 15)°
According to the exterior angle theorem:
m∠cde = m∠bcd + m∠dbc
(8x - 15)° = (3x + 11)° + (2x + 16)°
Combine like terms:
(8x - 15)° = (5x + 27)°
8x - 15 = 5x + 27
Solve for x:
3x = 42
x = 14
Therefore, the value of x is 14.