Question

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what is the measure of ∠bcd?
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the measure of ∠bcd = \\(\square\\)°
(image of a quadrilateral with vertices a, b, c, d, angle at b is 103° and arrow markings indicating its a parallelogram)

Explanation:

Step1: Identify the figure type

The figure is a parallelogram (opposite sides are parallel, indicated by the arrows). In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)).

Step2: Use the supplementary angle property

We know \(\angle B = 103^\circ\). Since \(\angle B\) and \(\angle BCD\) are consecutive angles in a parallelogram, they are supplementary. So, \(\angle BCD = 180^\circ - 103^\circ\).

Step3: Calculate the measure

\(180 - 103 = 77\).

Answer:

\(77\)