Question

Find the measure of arc DB.

25°
96°
118°
146°

Answer 1

146°

Explanation:

By the property of intersecting tangent and secant outside of a circle.

`(5x )\degree = (1)/(2) [(25x + 21) \degree - 96 \degree] \\ \\ (5x )\degree * 2= (25x + 21 - 96) \degree \\ \\ (10x )\degree = (25x + 21 - 96) \degree \\ \\ 10x = 25x - 75 \\ \\ 75 = 25x - 10x \\ \\ 75 = 15x \\ \\ x = (75)/(15) \\ \\ x = 5 \\ \\ m (\widehat{DB}) = (25x + 21) \degree \\ \\ m(\widehat{DB} )= (25 * 5 + 21) \degree \\ \\ m(\widehat{DB} )= (125 + 21) \degree \\ \\ \huge \purple{ \boxed{m( \widehat{DB} )= 146 \degree}} \\ \\`