Calculate Angle BCD in a Quadrilateral with 48° and 119° Given Angles

To solve this problem, follow these steps:

• Step 1: Identify all given angles and understand the setup.

• Step 2: Apply the sum of angles in a quadrilateral formula.

• Step 3: Calculate the unknown angle.

Now, let's solve:
Step 1: The problem states:

• $\angle \text{DAB} = 48^\circ$

• $\angle \text{ADC} = 119^\circ$

• $\angle \text{ABC} = 90^\circ$ since it's marked as a right angle.

Step 2: Use the sum of angles in quadrilateral $ABCD$: $\angle \text{DAB} + \angle \text{ABC} + \angle \text{BCD} + \angle \text{ADC} = 360^\circ$ Substituting the known values: $48^\circ + 90^\circ + \angle \text{BCD} + 119^\circ = 360^\circ$ Step 3: Simplify and solve for $\angle \text{BCD}$: $157^\circ + \angle \text{BCD} = 360^\circ$$\angle \text{BCD} = 360^\circ - 157^\circ = 203^\circ$ Therefore, the measure of $\angle \text{BCD}$ is $103^\circ$.

Thus, the size of angle $\angle \text{BCD}$ is $103^\circ$.