what is the measure of angle bcd? 25° 40° 140° 155°

Explanation:

Step1: Recall properties of a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Identify known angles

We know $\angle BAD = 25^{\circ}$, $\angle ABC=146^{\circ}$, $\angle ADC = 149^{\circ}$. Let $\angle BCD=x$.

Step3: Set up an equation

$25^{\circ}+146^{\circ}+149^{\circ}+x = 360^{\circ}$.

Step4: Simplify the left - hand side

$320^{\circ}+x=360^{\circ}$.

Step5: Solve for x

$x=360^{\circ}- 320^{\circ}=40^{\circ}$.

Answer:

$40^{\circ}$