Question

Help me find AD in degrees

Answer 1

43°

Explanation:

In circle with center P, AB is diameter. Hence,
`\widehat{ACB}` is a semicircular arc.

`\therefore \widehat{ACB}= 180\degree.... (1)\\</p><p>\because \widehat{ACB}= \widehat{AD} + \widehat{DC}+ \widehat{CB}.... (2)\\</p><p>From\: (1)\: \&\: (2)\\</p><p> \widehat{AD} + \widehat{DC}+ \widehat{CB} = 180\degree \\</p><p>\therefore (7x + 1)\degree + 90\degree + (9x-7)\degree = 180\degree \\</p><p></p><p>\therefore (16x - 6)\degree = 180\degree- 90\degree\\</p><p>\therefore (16x - 6)\degree = 90\degree\\</p><p>\therefore 16x - 6 = 90\\</p><p>\therefore 16x = 90 +6\\</p><p>\therefore 16x = 96\\\\</p><p>\therefore x = (96)/(16)\\\\</p><p>\huge \red {\boxed {\therefore x = 6}} \\</p><p>\therefore \widehat{AD} = (7x+1)\degree \\</p><p>\therefore \widehat{AD} = (7* 6+1)\degree \\</p><p>\therefore \widehat{AD} = (42+1)\degree \\</p><p>\huge \orange {\boxed {\therefore \widehat{AD} = 43\degree}} \\</p><p>`