Question

NEED HELP QUICKLYYY!!!!!!!!!!!!!!

the options under select are

40°

50°

55°

100°

Answer 1

The correct options are:

`m\angle ABD = 55^\circ`

`m\angle BDC = m\angle DBC = m\angle DCB = 50^\circ`

In Triangle ABD, we know that angle BAD is 45 degrees and angle BDA is 80 degrees. To find angle ABD, we can use the fact that the sum of angles in a triangle is 180 degrees. Therefore,

`m\angle ABD = 180^\circ - m\angle BAD - m\angle BDA`

`= 180^\circ - 45^\circ - 80^\circ`

`= 55^\circ`

Now, since Triangle BDC is isosceles, angles DBC and DCB are equal. Let's denote them as x.

`m\angle BDC = m\angle DBC = m\angle DCB = x`

Since the sum of angles in a triangle is 180 degrees,

`m\angle BDC + m\angle DBC + m\angle DCB = 180^\circ`

`x + x + 80^\circ = 180^\circ`

`2x + 80^\circ = 180^\circ`

`2x = 100^\circ`

`x = 50^\circ`

Now, let's complete the table:

`m\angle ABD = 55^\circ`

`m\angle BDC = m\angle DBC = m\angle DCB = 50^\circ`

`m\angle DBC = m\angle DCB = 50^\circ`

So, the correct options are:

`m\angle ABD = 55^\circ`

`m\angle BDC = m\angle DBC = m\angle DCB = 50^\circ`