Question

Question:

Answer 1

Answer:

Part 1) The draw in the attached figure

Part 2) $m\angle ABD=50^o$

Step-by-step explanation:

Part 1)  Draw the described circle

The draw in the attached figure

Part 2) What is the measure of angle ABD

step 1

Find the measure of arc AD

Remember that

$arc\ AD+arc\ DC+arc\ AC=360^o$ ----> by complete circle

substitute the given values

$arc\ AD+124^o+68^o=360^o$

$arc\ AD=360^o-192^o=168^o$

step 2

Find the measure of angle ABD

we know that

The measurement of the external angle is the half-difference of the arches that comprise

In this problem

The measure of angle ABD is an external angle

so

$m\angle ABD=\frac{1}{2} [arc\ AD-arc\ AC]$

substitute the given values

$m\angle ABD=\frac{1}{2} [168^o-68^o]=50^o$