Question

40. Assume the lines that appear to be tangent are tangent. O is the center of the circle. Findthe value of xmZP-12c. 102d. 24a. 78b. 39

Answer 1

Answer

a. 78

Step-by-step explanation

Given that side PQ is tangent to circle O, then angle Q measures 90 degrees.

The addition of the three interior angles of a triangle is equal to 180 degrees. Applying this to triangle PQO, we get:

$\begin{gathered} m\angle P+m\angle Q+m\angle O=180\degree \\ 12\degree+90\degree+x=180\operatorname{\degree} \\ x=180\operatorname{\degree}-12\degree-90\degree \\ x=78\operatorname{\degree} \end{gathered}$