Question

GEOMETRY)

Fill in the blanks:

How many degrees is arc PA?

How many degrees is angle PRA?

Line PR is a diameter of the circle. How many degrees is arc PAR?

How many degrees is arc AR?

(The picture is below and Q is the one above the circle and A at the bottom of the circle)

Answer 1

Part 1

By the inscribed angle theorem, arc PA measures 62 degrees.

Part 2

Angles inscribed in the same arc are congruent, so angle PRA measures 31 degrees.

Part 3

Diameters form semicircles, and the arc of a semicircle measures 180 degrees, so arc PAR measures 180 degrees.

Part 4

Subtracting arc PA from arc PAR, we get arc AR measures 118 degrees.