Please help with this arc equation.

Question

asked May 20, 2021 138k views

1 Answer

Ben Taber · Answer 1 · 2021-05-26T22:36:21+0000

Answer:

Part 1)
$arc\ AB=49^o$

Part 2)
$arc\ ABC=204^o$

Part 3)
$arc\ BAC=156^o$

Part 4)
$arc\ ACB=311^o$

Explanation:

Part 1) Find the measure of arc AB

we know that

$arc\ AB=m\angle AOB$ ----> by central angle

we have

$m\angle AOB=49^o$

therefore

$arc\ AB=49^o$

Part 2) Find the measure of arc ABC

we know that

The central angle of complete circle is equal to 360 degrees

so

$arc\ ABC=360^o-107^o-49^o=204^o$

Part 3) Find the measure of arc BAC

we know that

$arc\ BAC=arc\ BA+arc\ AC$ ----> by angle addition postulate

we have

$arc\ BA=49^o$ ---> by central angle

$arc\ AC=107^o$ ---> by central angle

so

$arc\ BAC=49^o+107^o=156^o$

Part 4) Find the measure of arc ACB

we know that

The central angle of complete circle is equal to 360 degrees

so

$arc\ ACB=360^o-arc\ AB$

substitute

$arc\ ACB=360^o-49^o=311^o$