In rectangle JKLM, with m‚à†KJM =…

Maths Questions

In rectangle JKLM, with m∠KJM = m∠KLM = 90° and m∠KJC + m∠MLC, which reason justifies the statement that m∠KLC is complementary to m∠KJC? 1) Angles that are congruent are complementary to the same angle. 2) Angles that are congruent are supplementary to the same angle. 3) All angles in a rectangle are right angles. 4) Complementary angles are always congruent.

Answer

Complementary angles are defined as two angles that sum to 90°, which represents a right angle, while supplementary angles total 180°, or a straight angle. Although these concepts may not seem exciting in geometry, recognizing them in diagrams and applying the relevant theorems in proofs is essential. The theorems pertinent to complementary angles are: Complements of the same angle are congruent, meaning if two angles are both complementary to a third angle, they are congruent to each other (involving three angles). Additionally, complements of congruent angles are congruent, indicating that if two angles are complementary to two other congruent angles, those angles must be congruent as well (involving four angles). Therefore, the justified reason is: Angles that are congruent are complementary to the same angle.

Scroll to Top