Question

can two angles of a kite be consecutive and supplementary? explain.

choose the correct answer below.

a. no, because if two consecutive angles are supplementary, then another pair of consecutive angles are also supplementary. therefore, the consecutive angles must be right angles. the figure would have to be a rectangle.

b. yes, because if two consecutive angles are supplementary, the other pair of consecutive angles are also supplementary. therefore, a pair of opposite angles can be congruent, which is a kite.

c. yes, because if two consecutive angles are supplementary, then another pair of consecutive angles are also supplementary. therefore, the sum of the angles is 360°.

d. no, because if two consecutive angles are supplementary, then another pair of consecutive angles are also supplementary. since a kite has one pair of congruent opposite angles, then two pairs of opposite angles must be congruent. the figure would have to be a parallelogram.

Explanation:

A kite has one pair of congruent opposite angles. If two consecutive angles are supplementary, the adjacent sides are parallel (since consecutive angles between parallel lines are supplementary). For a kite, this parallelism can coexist with one pair of congruent opposite angles, satisfying the kite definition. Option B correctly states this logic.

Answer:

B. Yes, because if two consecutive angles are supplementary, the other pair of consecutive angles are also supplementary. Therefore, a pair of opposite angles can be congruent, which is a kite.