Problem Analysis:
The image shows a right triangle \( \triangle ABC \) with the following details:
- \( \angle ABC = 90^\circ \) (indicated by the red square at vertex \( B \)).
- \( \angle BAC = 45^\circ \).
- \( \angle BCA = 45^\circ \).
The task is to analyze the given angles and determine if they form complementary angle pairs. Complementary angles are two angles whose measures add up to \( 90^\circ \).
Step-by-Step Solution:
1.
Identify the Angles in the Triangle:
- The triangle \( \triangle ABC \) is a right triangle with \( \angle ABC = 90^\circ \).
- The other two angles are \( \angle BAC = 45^\circ \) and \( \angle BCA = 45^\circ \).
2.
Check for Complementary Angle Pairs:
-
Definition of Complementary Angles: Two angles are complementary if their measures add up to \( 90^\circ \).
3.
Analyze the Angles:
-
Pair 1: \( \angle BAC \) and \( \angle BCA \)
\[
\angle BAC + \angle BCA = 45^\circ + 45^\circ = 90^\circ
\]
These two angles are complementary.
-
Pair 2: \( \angle BAC \) and \( \angle ABC \)
\[
\angle BAC + \angle ABC = 45^\circ + 90^\circ = 135^\circ
\]
These two angles are not complementary.
-
Pair 3: \( \angle BCA \) and \( \angle ABC \)
\[
\angle BCA + \angle ABC = 45^\circ + 90^\circ = 135^\circ
\]
These two angles are not complementary.
4.
Conclusion:
- The only pair of complementary angles in the triangle is \( \angle BAC \) and \( \angle BCA \).
Final Answer:
\[
\boxed{\angle BAC \text{ and } \angle BCA}
\]
Parent Tip: Review the logic above to help your child master the concept of angle pair worksheets.
