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given: m∠dea=46°, m∠p=14°
find the measurements of arc ad and arc bc.

The measurement of arc AD is 53°

The measurement of arc BC is 39°

Step-by-step explanation:

Let

x> the measurement of arc AD

y---> the measurement of arc BC

we know that

The measure of the internal angle is the semi-sum of the arcs comprising it and its opposite

so

m∠DEA=(1/2)[x+y]

substitute the value

46°=(1/2)[x+y]

92°=[x+y] > equation A

The measurement of the external angle is the semi-difference of the arcs which comprises

m∠P=(1/2)[x-y]

substitute the value

14°=(1/2)[x-y]

28°=[x-y] > equation B

Adds equation A and equation B

92°+14°=2x

x=106°/2=53°

Find the value of y

substitute in the equation A the value of x

92°=[53°+y]

y=92°-53°=39°

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