Question

If arc CB equals 5x+41, arc AD equals 7x-19, and angle AED equals 89 degrees, find arc AD.

Answer 1

Answer:

arc AD = 72°

Step-by-step explanation:

Consider the below figure attached with the question.

If two chords intersect each other inside the circle, then

$\text{Angle inside}=\dfrac{1}{2}(\text{Sum of intercepted arcs})$

For the given figure,

$\angle AED=\dfrac{1}{2}(Arc(AD)+Arc(CB))$

$89=\dfrac{1}{2}(7x-19+5x+41)$

$89=\dfrac{1}{2}(12x+22)$

$89=6x+11$

$89-11=6x$

$78=6x$

$13=x$

The value of x is 13.

$Arc(AD)=7x-19=7(13)-19=91-19=72$

Therefore, the measure of arc AD is 72°.