Question

Select the correct answer from each drop down menu.

Answer 1

1. While turning clockwise, AB must cover up 63.9° in order to coincide with BC.
2. While turning counter clockwise, AB must cover up 116.1° in order to coincide with BE.

Solution-

From the attachment,

∠ABC is made up of two acute angles i.e ∠ABD and ∠DBC

Hence,

`\Rightarrow m\angle ABC=m\angle ABD+m\angle DBC\\\\\Rightarrow m\angle ABC=33.3^(\circ)+30.6^(\circ)=63.9^(\circ)`

So, while turning clockwise, AB must cover up 63.9° in order to coincide with BC.

As B, E, C are co-linear, so ∠ABE and ∠ABC are complimentary angles.

Hence,

`\Rightarrow m\angle ABE+m\angle ABC=180^(\circ)\\\\\Rightarrow m\angle ABE=180^(\circ)-m\angle ABC\\\\\Rightarrow m\angle ABE=180^(\circ)-63.9^(\circ)\\\\\Rightarrow m\angle ABE=116.1^(\circ)`

So, while turning counter clockwise, AB must cover up 116.1° in order to coincide with BE.