Definition of Complementary Angles
Angles ∠_DEB_ and ∠_BEF_ are 90° angles.
| Quantity A | Quantity B |
|------------|------------|
|∠_AEB_ |∠_BEC_ |
Incorrect.
[[snippet]]
Notice that ∠_DEA_ and ∠_AEB_ are complementary angles. So ∠_AEB_ = 90° - ∠_DEA_ = 90° - 36° = 54°.
Use similar reasoning to find the value of ∠_BEC_ (Quantity B) Then, compare the two values.
Correct.
Notice that ∠_DEA_ and ∠_AEB_ are complementary angles. Therefore, the sum of their degree measurements is 90°. So ∠_AEB_ = 90° - ∠DEA = 90° - 36° = 54°.
Similarly, ∠_BEC_ and ∠_CEF_ are complementary angles. So the sum of their degree measurements is 90°. Therefore, ∠_BEC_ = 90° - ∠_CEF_ = 90° - 29° = 61°.
Therefore ∠_BEC_ (Quantity B) is greater than ∠_AEB_.
Incorrect.
[[snippet]]
Notice that ∠_DEB_ = 90° and ∠_BEF_ = 90°. Since the values of ∠_DEA_ and ∠_CEF_ are not equal, the values of ∠_AEB_ and ∠_BEC_ also cannot be equal.
Incorrect.
[[snippet]]
∠_DEB_ = 90°. Since ∠_DEB_ is comprised of ∠_DEA_ and∠_AEB_, and the value of ∠_DEA_ is given, use what you know about complementary angles to find the value of ∠_AEB_.
Similar reasoning can be used to find ∠_BEC_. Once both values are found, comparison is possible.
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
