Question

Determine the measure of angle P if the measure of arc BD is 154 degrees and secant AD is a diameter of Circle C.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The angle P is  $P = 26^o$

Step-by-step explanation:

From the question we are told that

    The angle BD is  $BD = 154^o$

Now looking at the diagram we can deduce that angle $B \r CD = 180 ^o$

Now looking at line AD we see that it is tangent to the circle this implies that line CD is perpendicular to line AD

   So  we can also deduce that

            $B \r C A + D \r C A = 180$

=>       $D \r C A = 180 - 154$

=>       $D \r C A = 26^o$

 Now total angle in a triangle is 180 so

        $C\r DA + D\r A C + A \r C D = 180^o$

Now  $D \r A C = 90^o$

So  

          $D \r AC = 180 - (90 + 26)$

=>      $P = D \r AC = 26^o$