The measurement of angle JPV from the considered situation is found as m∠JPV = 106°
What is the angle the radius makes on the point of contant of a tangent of a circle?
The radius which touches the point where the tangent touches too on a specified circle, is perpendicular to the tangent (90 degrees angle with the tangent).
Referring to the image attached below, we're provided that:
m arcVKP = central angle arc VKP subtends = m∠VOP = 148°
The perpendicular from center O on the line VP (VP is a chord) bisects it, and therefore, the triangle ODP and ODV are congruent by SAS congruency [ side OD is common, the angle (the 90 degree) on either side of OD is of same measure, and VD and DP are of same measure due to OD bisecting VP).
Thus, we get:
[tex]m\angle POD = m\angle VOD[/tex]
But since we have:
m∠POD + m∠VOD = m∠VOP = 148°
thus, m∠POD + m∠POD = 148°
or m∠POD = 148°/2 = 74° = m∠VOD
Now, as sum of angles in a triangle is 180°, therefore, for triangle OPD, we get:
[tex]m\angle OPD + m\angle ODP + m\angle POD = 180^\circ\\x^\circ + 90^\circ + 74^\circ = 180^\circ\\x = 16[/tex]
Thus, we get the measurement of angle JPV as:
[tex]m\angle JPV = m\angle JPO + m\angle OPD\\ m\angle JPV = 90^\circ + x^\circ = (90 + 16)^\circ = 106^\circ[/tex]
Thus, the measurement of angle JPV from the considered situation is found as m∠JPV = 106°
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