Question

if ∠acd and ∠bac are alternate interior angles and ( mangle acd = 101^circ ), what is the measure of ( angle bac )?
a. ( 79^circ )
b. ( 259^circ )
c. ( 11^circ )
d. ( 101^circ )

Explanation:

Step1: Recall Alternate Interior Angles

Alternate interior angles are supplementary (sum to \(180^\circ\)) when lines are parallel? Wait, no—wait, alternate interior angles are equal when lines are parallel, but if they are same - side interior angles, they are supplementary. Wait, the problem says \(\angle ACD\) and \(\angle BAC\) are alternate interior angles? Wait, no, maybe there's a mis - read. Wait, actually, if two angles are same - side interior angles (consecutive interior angles), they are supplementary. Wait, maybe the problem has a typo, but assuming that \(\angle ACD\) and \(\angle BAC\) are same - side interior angles (since alternate interior angles are equal, but \(101^\circ\) and \(101^\circ\) would not be supplementary, but if they are same - side, then \(\angle BAC=180^\circ - 101^\circ\)).

Step2: Calculate \(\angle BAC\)

We know that if two angles are supplementary, their sum is \(180^\circ\). Let \(m\angle BAC = x\). Then \(x+101^\circ = 180^\circ\). Solving for \(x\), we get \(x = 180^\circ- 101^\circ=79^\circ\).

Answer:

A. \(79^\circ\)