Quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle o? you must show all work and calculations to receive credit. (10 points)

A quadrilateral inscribed in a circle is called a "cyclic quadrilateral."

A quadrilateral is cyclic, only if the sum of the measures of the opposite angles is 180°. 

Also, the reverse is true: If we know a quadrilateral to be cyclic, than its opposite angles must be supplementary (add up to 180°) .

Thus, we must have:



2x+(2x+4)=180

4x+4=180 (next dividing by 4:)

x+1=45

Thus, x=44, which means that the measure of angle O is 2x degrees, that is 88 degrees.

88°

Okay so for every triangle has three angles that always add up to 180 degrees. and to tell the difference between whether they are secure, right or obtuse is that acute: has one angle that is less than 90 degrees. right triangle means there is at least one angle that is exactly 90 degrees. and an obtuse angle has an angle that is bigger than 180 degrees. i’ll do #13 as an example: 13. 40 and 50 so if every triangle has 180 degrees 40+50= 90 degrees then180-90= 90 degrees so the third angle is 90 degrees and because this triangle has a 90 degree angle it means it is a right triangle