Question

Help me find AD in degrees

Answer 1

Answer:

43°

Step-by-step explanation:

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

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