Question

Please help me solve this problem, an explanation would be very helpful

Answer 1

Given that:

`AB\perp BD`

And given that these angles are Complementary (they add up to 90 degrees):

`\begin{gathered} \angle EFG \\ \angle ABC \end{gathered}`

22. A Right Angle is an angle that measures 90 degrees. Therefore, by the definition of Right Angles:

`\angle ABD=90°`

23. According to the Angle Addition Postulate, if two or more angles are next to each other and have a common vertex, then the total measure of the angle is obtained by adding them.

Therefore, in this case:

`m\angle ABC+m\angle CBD=m\angle ABD`

24. The Substitution Property of Equality states that, if:

`a=b`

And:

`a=c`

Then:

`b=c`

Applying that property, you can set up that:

`m\angle ABC+m\angle CBD=90\text{\degree}`

25. By definition, Complementary Angles add up to 90 degrees.

Knowing that angles EFG and ABC are Complementary, you know that:

`\angle EFG+\angle CBD=90°`

26. The Transitive Property of Equality states that if:

`a=b`

And:

`b=c`

Then:

`a=c`

Therefore:

`\angle ABC+\angle CBD=\angle EFG+\angle CBD`

27. According to the Congruent Complements Theorem, two angles have the same measure of they are complementary to the same angles. In this case:

`\angle ABC=\angle EFG`

28. By definition, if two angles are congruent, they have the same measure.

Hence, the answer is.

22. Definition of Right Angles.

23.

`m\angle ABC+m\angle CBD=m\angle ABD`

24. Substitution Property of Equality.

25. Definition of Complementary Angles.

26 Transitive Property of Equality.

27. Congruent Complements Theorem.

28. Congruence Definition.