Question

In parallelogram ABCD 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?

1) 26°
2) 41°
3) 52°
4) 67°

Answer 1

The measure of angle BCA in parallelogram ABCD is 41°. This is found by using the fact that opposite angles in a parallelogram are equal and the sum of angles in a triangle equals 180°.

Step-by-step explanation:

To find the measure of angle BCA in parallelogram ABCD with diagonal AC, we can use the properties of parallelograms. The fact that angle DCA is 26° and angle ABC is 113° provides us with the necessary information to solve the problem.

In a parallelogram, opposite angles are equal. Therefore, angle DCA is equal to angle BAC. Since we know that angle DCA is 26°, angle BAC is also 26°. Now, let's focus on triangle ABC formed by diagonal AC. We know that angle ABC is 113°, and we just deduced that angle BAC is 26°. Since the sum of angles in any triangle is 180°, we can now find the measure of angle BCA:

180° - (angle ABC + angle BAC) = 180° - (113° + 26°) = 180° - 139° = 41°

Therefore, the measure of angle BCA is 41°.