Question

Quadrilateral ABCD is a rhombus. suppose measure of angle A decreases. Which of the following changes woukd also need to happen in order for ABCD to still be a rhombus

Answer 1

Explanation:

Given that quadrilateral ABCD is a rhombus. Given that angle A decreases.

Since nothing is mentioned about the side of the rhombus, we see that side is not changing.

When angle A decreases, since opposite angles are congruent we must have equal decrease in C

Also opposite sides are parallel in a rhombus, hence adjacent angles are supplementary.

i.e. Whenever A decreases by a quantity say p, then B and D, the adjacent angles must increase by same quantity p so that the parallel lines property is preserved in the rhombus.

Answer 2

Assuming the side lengths did not change, ...

Angle C would need to decrease by the same amount.
Angles B and D would each need to increase by the amount angle A decreased.