Question

Given the following diagram, if m∠1 = m∠4, then all of the following must be complementary angles except

angles 1 and 2
angles 1 and 3
angles 2 and 3
angles 2 and 4

Answer 1

There is missing info is this problems to be sire f m∠1 = m∠4, then all of the following must be complementary angles except and that is that line bf and AD are perpendicular. However if we presume that

Complementary means they add to 90 so if 1 and 4 are equal then so are 2 and 3 and 2 and 3 are equal. However 2 and 3 are not complementary

Answer 2

Option C

Explanation:

We are given that
`m\angle 1=m\angle m`

We have to find that which pair of angles is not complementary

OD is perpendicular to FB

Therefore,
`m\angle 1+m\angle 2=90^(\circ)`

`m\angle 3+m\angle 4=90^(\circ)`

Substitute the values then we get

`m\angle 4+m\angle 2=90^(\circ)` (
`m\angle 1=m\angle4`)

`m\angle 4+m\angle 3=m\angle 2+m\angle 4`

`m\angle 3=m\angle 2`

Substitute the value then we get

`m\angle 1+m\angle 3=90^(\circ)`

`m\angle 2+m\angle 4=90^(\circ)`

Complementary angles are that angles whose two angles sum is 90 degrees.

Hence, angle 2 and angle 3 are not complementary angles.

Option C is true.