Assume that lines that appear to be tangent are tangent. Point O is the center of the circle. Find the value of x if the m<P = 28

1 answer

Since line segment $\overline{QP}$ is tangent to the circle, we know that the radius of the circle is perpendicular to the tangent line at the point of tangency. Therefore, $\angle POQ$ is a right angle.

Since $\angle POQ$ is a right angle, we know that the sum of $\angle PQO$ and $\angle OQP$ is equal to 90 degrees.

Given that $\angle P = 28$ degrees, we can express $\angle PQO$ as 28 degrees and $\angle OQP$ as $90 - 28 = 62$ degrees.

Finally, we can calculate the value of $x$ as follows:

$x = \angle QOP = \angle PQO + \angle OQP = 28 + 62 = 90$ degrees

Therefore, the value of $x$ is 90 degrees.