1 Answer

Delusional Logic · Answer 1 · 2022-12-08T05:10:24+0000

Given:

The figure of a circle.

To find:

The measure of arc AD and measure of each arc.

Solution:

The measure of arc is equal to the central angle of that arc.

The central angle of arc AD is 105 degrees. So,

$m(arc(AD))=105^\circ$

The central angle of arc BC is 35 degrees. So,

$m(arc(BC))=35^\circ$

The central angle of arc CD is 50 degrees. So,

$m(arc(CD))=50^\circ$

The central angle of a complete circle is 360 degrees. So,

$m(arc(AD))+m(arc(BC))+m(arc(CD))+m(arc(AB))=360^\circ$

$105^\circ+35^\circ+50^\circ+m(arc(AB))=360^\circ$

$190^\circ+m(arc(AB))=360^\circ$

$m(arc(AB))=360^\circ-190^\circ$

$m(arc(AB))=170^\circ$

Therefore, the measure of arc AD is 105°, the measure of arc BC is 35°, the measure of arc CD is 50° and the measure of arc AB is 170°

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