I've got a few geometry homework questions about arcs, and I'm not too sure about how to solve them.
7: In rectangle PQRS, PS=3 and PQ=4. Let M be the midpoint of line PQ , and let X be the point such that MS=MX and angle MSX=77 degrees, as shown below. Find angle XRS, in degrees.
Angle XRS works out to 77 - 60 = 17 degrees.
With M as a center, construct a circle with radius MS
This circle will pass through S , X and R
Since MS = MX, then angles MSX and MXS are equal
So triangle MSX is isosceles .....so angle SMX = [ 180 - 2(77) ] = 26°
And this is a central angle in the circle that intercepts minor arc SX
And angle XRS is an inscribed angle in the circle that intercepts this same arc
So....the measure of angle XRS = (1/2)26° = 13°