Question

Given: ZCAT and ZDOG are right angles. What are ALL the conclusions that can be made?

A. ZCAT and ZDOG are complementary angles.
B. ZCAT and ZDOG are supplementary angles.
C. ZCAT and ZDOG are right angles.
D. ZCAT and ZDOG are congruent.

Answer 1

ZCAT and ZDOG are right angles, which means they are each 90°. Since all right angles are equal in measure, they are also congruent to each other. They are not complementary, and their being supplementary is conditional on adjacency, which is not given.

Step-by-step explanation:

Given that ZCAT and ZDOG are right angles, several conclusions can be drawn. Since right angles are 90° by definition, we know that:

• ZCAT and ZDOG are not complementary angles, as complementary angles sum to 90° and each of these angles is already 90° on its own.
• ZCAT and ZDOG would be supplementary angles if they were adjacent, as supplementary angles sum to 180°. However, the problem does not specify that these angles are adjacent.
• Clearly, ZCAT and ZDOG are right angles; this is given in the problem statement.
• Since all right angles are equal in measure (90°), ZCAT and ZDOG are also congruent.

Therefore, the correct conclusions based on the given information are C, ZCAT and ZDOG are right angles, and D, ZCAT and ZDOG are congruent.