Question

Please look at the screenshot

Answer 1

Given:

The figure of circle E. $m\angle ABD=(11x-3)^\circ,m\angle ACD=(8x+15)^\circ$.

To find:

The measure of arc AD.

Solution:

We know that the inscribed angles on the same arc are congruent and their measures are equal.

$\angle ABD$ and $\angle ACD$ are inscribed angles on the same arc AD. So,

$m\angle ABD=m\angle ACD$

$11x-3=8x+15$

$11x-8x=3+15$

$3x=18$

$x=6$

Now,

$m\angle ABD=(11x-3)^\circ$

$m\angle ABD=(11(6)-3)^\circ$

$m\angle ABD=(66-3)^\circ$

$m\angle ABD=63^\circ$

We know that the intercepted arc is always twice of the inscribed angle.

$m(Arc(AD))=2\times m\angle ABD$

$m(Arc(AD))=2\times 63^\circ$

$m(Arc(AD))=126^\circ$

Therefore, the measure of arc AD is 126 degrees.