Question

in parallelogram abcd, diagonals ac and bd intersect at point e. if ∠dac = 75°, what is the measure of ∠bca?
a. 60°
b. 75°
c. 90°

Explanation:

Step1: Recall parallelogram property

In parallelogram \(ABCD\), \(AD\parallel BC\).

Step2: Use alternate - interior angles

\(\angle DAC\) and \(\angle BCA\) are alternate - interior angles formed by the transversal \(AC\) intersecting parallel lines \(AD\) and \(BC\). Alternate - interior angles are congruent when two parallel lines are cut by a transversal. So \(\angle BCA=\angle DAC\).

Step3: Substitute the given angle measure

Since \(\angle DAC = 75^{\circ}\), then \(\angle BCA=75^{\circ}\).

Answer:

B. \(75^{\circ}\)