Question

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Answer 1

Answer: The measure of non-reflex ∠DOB is 108° and the measure of reflex ∠DOB is 252°.

Explanation:

It is given that the reflex angle ∠DOB has measure of 3.5y while the measure of ∠AOD is y.

From the given figure we can say that angle AOC and COB are supplementary angles and their sum is 180 because they are lies on a straight line.

$\angle DOB=\angle AOD+\angle AOC+\angle COB$

$3.5y=y+180$

$3.5y-y=180$

$2.5y=180$

$y=72$

Therefore the value of y is 72.

$\angle DOB=3.5y$

$\angle DOB=3.5\times 72$

$\angle DOB=252$

Therefore the reflex and is 252 degree.

The measure of non-reflex ∠DOB is,

$\angle DOB=360-252=108^{\circ}$

Therefore, the  measure of non-reflex ∠DOB is 108° and the measure of reflex ∠DOB is 252°.