Answer:
43°
Step-by-step explanation:
In circle with center P, AB is diameter. Hence, [tex] \widehat{ACB} [/tex] is a semicircular arc.
[tex] \therefore \widehat{ACB}= 180\degree.... (1)\\
\because \widehat{ACB}= \widehat{AD} + \widehat{DC}+ \widehat{CB}.... (2)\\
From\: (1)\: \&\: (2)\\
\widehat{AD} + \widehat{DC}+ \widehat{CB} = 180\degree \\
\therefore (7x + 1)\degree + 90\degree + (9x-7)\degree = 180\degree \\
\therefore (16x - 6)\degree = 180\degree- 90\degree\\
\therefore (16x - 6)\degree = 90\degree\\
\therefore 16x - 6 = 90\\
\therefore 16x = 90 +6\\
\therefore 16x = 96\\\\
\therefore x = \frac{96}{16}\\\\
\huge \red {\boxed {\therefore x = 6}} \\
\therefore \widehat{AD} = (7x+1)\degree \\
\therefore \widehat{AD} = (7\times 6+1)\degree \\
\therefore \widehat{AD} = (42+1)\degree \\
\huge \orange {\boxed {\therefore \widehat{AD} = 43\degree}} \\
[/tex]
