Question

question 4 (multiple choice worth 1 points) abcd is a parallelogram with diagonal ac. if the measure of angle dca is 26° and the measure of angle abc is 113°, what is the measure of angle bca?

Explanation:

Step1: Recall property of parallelogram

In parallelogram \(ABCD\), \(\angle ABC+\angle BAD = 180^{\circ}\) (adjacent - angles are supplementary).
Since \(\angle ABC = 113^{\circ}\), then \(\angle BAD=180 - 113=67^{\circ}\).

Step2: Use property of parallel - lines

In parallelogram \(ABCD\), \(AB\parallel CD\), so \(\angle BAC=\angle DCA = 26^{\circ}\) (alternate - interior angles).

Step3: Calculate \(\angle BCA\)

We know that \(\angle BAC+\angle BCA=\angle BAD\). Let \(\angle BCA=x\). Then \(26 + x=67\). Solving for \(x\), we get \(x=\angle BCA=67 - 26=41^{\circ}\).

Answer:

\(41^{\circ}\)