SOLUTION: The center of the circle is O, angle TQR = 46 degrees and angle QTO = 51 degrees. Find the measure of angle RPO. Link to graph: https://ibb.co/bmnmVgb

Question 1209480: The center of the circle is O, angle TQR = 46 degrees and angle QTO = 51 degrees.
Find the measure of angle RPO.
Link to graph: https://ibb.co/bmnmVgb
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The measure of angle TQR is given as 46 degrees, so the measure of angle TQP is 180-46 = 134 degrees.

That means the measure of major arc PT is 2*134 = 268 degrees.

That in turn means the measure of minor arc PT is 360-368 = 92 degrees.

And since central angle POT cuts off minor arc PT, the measure of angle POT is 92 degrees.

The measure of angle QTO was given as 51 degrees.

Now we have the measures of three of the four angles in quadrilateral POTQ, so the measure of angle RPO (= measure of angle QPO) is 360-(134+51+92) = 83 degrees.

ANSWER: 83 degrees

RELATED QUESTIONS
In triangle ABC, if angle A = 51 degrees and angle B = 73 degrees, what is the measure of (answered by Alan3354)

the measure of angle m is 46 degrees more then angle m what is angle... (answered by Alan3354,ikleyn)

The measure of angle XYZ is 46 degrees more than the measure of its supplement. Find... (answered by drj)

The Complement of angle M is 46 degrees more then angle M. Find the measure of angle... (answered by nerdybill)

the complement of angle m is 46 more degrees more than angle m find the measure of angle... (answered by stanbon)

If the measure of angle 3 equals 46 degrees then the measure of angle 6 is (answered by ikleyn)

The measure of an angle is 46 degrees less than the measure of its supplement. find the... (answered by checkley77)

In the diagram of circle O, AB and BC are chords and the measure of angle AOC= 136... (answered by anantha)

the complment of an angle is 46 degrees. what is the measure of the... (answered by Alan3354)