Question

ABCD is a parallelogram. the diagram is not drawn to scale. if m angle CDA= 128 degrees, then m angle DAB= _____?

Answer 1

DAB must equal 52 because same side interior angles are supplementary. Supplementary describes 2 angles whose measures add up to 180

Answer 2

`52^(\circ)`

Explanation:

By the properties of the parallelogram, we know that the consecutive angles are supplementary. That is, the sum of the consecutive angles is 180 degrees.

Here in the parallelogram ABCD, we have been given that the measure of angle CDA is 128 degrees, that is
`\measuredangle D=128^(\circ)`

Observe that in the parallelogram ABCD, the angle DAB or angle A is adjacent to angle CDA.

So angle DAB and angle CDA are consecutive and hence they are supplementary. So we have

`\angle DAB+\angle CDA=180^(\circ)\\\\\Rightarrow \angle DAB+128^(\circ)=180^(\circ)\\\\\Rightarrow \angle DAB=180^(\circ)-128^(\circ)\\\\\Rightarrow \angle DAB=52^(\circ)\\`