Question

Given: mEDF = 120°; mADB = (3x)°; mBDC = (2x)°Prove: x = 24What is the missing reason in step 3?vertical angles are congruentsubstitutiondefinition of congruencydefinition of equality

Answer 1

Please find the attachment for the accompanying diagram of this question. From the diagram we can see that
`\angle EDF` and
`\angle ADC` are vertically opposite angles.

Thus,
`\angle EDF=\angle ADC`

Now, we know that the value of
`\angle EDF`=120 degrees (given)

We also know that
`\angle ADC` is the sum of two angles,
`\angle ADB` and
`\angle BDC`, thus we have:

120=
`\angle ADB` +
`\angle BDC`

Now we are given that
`\angle ADB`=3x and
`\angle BDC`=2x, thus the above equation becomes

`120=3x+2x`

`5x=120`

therefore x=24

Thus we have proved that x=24 degrees as required