Answer:
[tex]m\widehat {EB}[/tex] = 96°
Step-by-step explanation:
From the figure attached,
m∠ECB = 25°
[tex]m\widehat {EB}={(4x+16)}[/tex] degrees
[tex]m\widehat{DB}=(7x+6)[/tex] degrees
From the theorem of secants intersecting outside the circle,
m∠ECB = [tex]\frac{1}{2}[m\widehat {DB}-m\widehat{EB}][/tex]
25° = [tex]\frac{1}{2}[(7x + 6) - (4x + 16)][/tex]
25° = [tex]\frac{1}{2}(3x-10)[/tex]
50 = 3x - 10
3x = 60
x = [tex]\frac{60}{3}[/tex]
x = 20
[tex]m\widehat {EB}[/tex] = (4 × 20 + 16)°
= (80 + 16)°
= 96°
Therefore, measure of arc EB is 96°.
