Answer:
[tex]m(BC) = 72^\circ[/tex]
[tex]m\angle EBC = 168^\circ[/tex]
Step-by-step explanation:
Given
[tex]m\angle BAC = 72[/tex]
[tex]m(BE) = 96[/tex]
See attachment for circle
Required
Determine
(a) Measure of BC
(b) Measure of EBC
(a) Measure of BC
From the attachment, we can see that:
[tex]m(BC) = m\angle BAC[/tex] because they belong to the same sector
This gives:
[tex]m(BC) = 72^\circ[/tex]
(b) Measure of EBC
From the attachment, we can see that:
[tex]m\angle EBC = m(EB) +m(BC)[/tex]
Where
[tex]m(EB) = m(BE) =96^\circ[/tex]
So, we have:
[tex]m\angle EBC = 96^\circ + 72^\circ[/tex]
[tex]m\angle EBC = 168^\circ[/tex]
