Question

Find the measure of arc EB. Circle A is intersected by line CD at points D and E and line CB at point B, forming angle ECB outside of the circle, the measure of angle ECB is 25 degrees, arc EB is 4x plus 16 degrees, and arc DB 7x plus 6 degrees.

Answer 1

96°

Explanation:

Got it right on the test

Answer 2

`m\widehat {EB}` = 96°

Explanation:

From the figure attached,

m∠ECB = 25°

`m\widehat {EB}={(4x+16)}` degrees

`m\widehat{DB}=(7x+6)` degrees

From the theorem of secants intersecting outside the circle,

m∠ECB =
`(1)/(2)[m\widehat {DB}-m\widehat{EB}]`

25° =
`(1)/(2)[(7x + 6) - (4x + 16)]`

25° =
`(1)/(2)(3x-10)`

50 = 3x - 10

3x = 60

x =
`(60)/(3)`

x = 20

`m\widehat {EB}` = (4 × 20 + 16)°

= (80 + 16)°

= 96°

Therefore, measure of arc EB is 96°.