Question

parallelogram abcd is shown.
what is ( mangle bac )?
( mangle bac = square )

Explanation:

Step1: Identify parallel line property

In parallelogram \(ABCD\), \(BC \parallel AD\), so alternate interior angles \(\angle CBD = \angle ADB = 27^\circ\).

Step2: Calculate \(\angle ABD\)

In \(\triangle ABD\), use angle sum:
\(\angle ABD = 180^\circ - 71^\circ - 27^\circ = 82^\circ\)

Step3: Isolate \(\angle BAC\)

\(\angle ABD = \angle ABC = \angle ABD_{total}\), so \(\angle BAC = \angle ABD - \angle CBD_{given}\)
\(\angle BAC = 82^\circ - 45^\circ = 37^\circ\)

Answer:

\(37^\circ\)