Find the measure of arc DB.
25°
96°
118°
146°
1 answer:
Answer:
146°
Step-by-step explanation:
By the property of intersecting tangent and secant outside of a circle.
![(5x )\degree = \frac{1}{2} [(25x + 21) \degree - 96 \degree] \\ \\ (5x )\degree \times 2= (25x + 21 - 96) \degree \\ \\ (10x )\degree = (25x + 21 - 96) \degree \\ \\ 10x = 25x - 75 \\ \\ 75 = 25x - 10x \\ \\ 75 = 15x \\ \\ x = \frac{75}{15} \\ \\ x = 5 \\ \\ m (\widehat{DB}) = (25x + 21) \degree \\ \\ m(\widehat{DB} )= (25 \times 5 + 21) \degree \\ \\ m(\widehat{DB} )= (125 + 21) \degree \\ \\ \huge \purple{ \boxed{m( \widehat{DB} )= 146 \degree}} \\ \\](https://tex.z-dn.net/?f=%285x%20%29%5Cdegree%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%5B%2825x%20%2B%2021%29%20%5Cdegree%20-%2096%20%5Cdegree%5D%20%20%5C%5C%20%20%5C%5C%20%285x%20%29%5Cdegree%20%20%5Ctimes%202%3D%20%2825x%20%2B%2021%20-%2096%29%20%5Cdegree%20%20%5C%5C%20%20%5C%5C%20%2810x%20%29%5Cdegree%20%20%3D%20%2825x%20%2B%2021%20-%2096%29%20%5Cdegree%20%20%5C%5C%20%20%5C%5C%2010x%20%3D%2025x%20-%2075%20%5C%5C%20%20%5C%5C%2075%20%3D%2025x%20-%2010x%20%5C%5C%20%20%5C%5C%2075%20%3D%2015x%20%5C%5C%20%20%5C%5C%20x%20%3D%20%20%5Cfrac%7B75%7D%7B15%7D%20%20%5C%5C%20%20%5C%5C%20x%20%3D%205%20%5C%5C%20%20%5C%5C%20m%20%20%28%5Cwidehat%7BDB%7D%29%20%3D%20%2825x%20%2B%2021%29%20%5Cdegree%20%5C%5C%20%20%5C%5C%20m%28%5Cwidehat%7BDB%7D%20%29%3D%20%2825%20%5Ctimes%205%20%2B%2021%29%20%5Cdegree%20%5C%5C%20%20%5C%5C%20%20m%28%5Cwidehat%7BDB%7D%20%29%3D%20%28125%20%2B%2021%29%20%5Cdegree%20%5C%5C%20%20%5C%5C%20%5Chuge%20%20%5Cpurple%7B%20%5Cboxed%7Bm%28%20%5Cwidehat%7BDB%7D%20%29%3D%20146%20%5Cdegree%7D%7D%20%5C%5C%20%20%5C%5C%20)
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