Question

Find <ABC + <ADChelp... ASAP! :)​

Answer 1

Answer:

Option D. 124°

Step-by-step explanation:

step 1

Find the measure of angle AOC

The triangle AOC is an isosceles triangle, because OA=OC=radius

so

$m\angle OAC=m\angle OCA=28^o$

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

$m\angle OAC+m\angle OCA+m\angle AOC=180^o$

substitute the given values

$28^o+28^o+m\angle AOC=180^o$

$56^o+m\angle AOC=180^o$

$m\angle AOC=180^o-56^o$

$m\angle AOC=124^o$

step 2

Find the measure of arc AC

we know that

$arc\ AC=m\angle AOC$ ----> by central angle

we have

$m\angle AOC=124^o$

therefore

$arc\ AC=124^o$

step 3

we know that

The inscribed angle is half that of the arc comprising

$m\angle ABC=\frac{1}{2}[arc\ AC]$

$m\angle ADC=\frac{1}{2}[arc\ AC]$

so

$m\angle ABC=m\angle ADC$

therefore

$m\angle ABC+m\angle ADC=2m\angle ABC=arc\ AC$

substitute the value of the arc AC

$m\angle ABC+m\angle ADC=124^o$