#1**+2 **

Hey, RP....good to see you !!!

First one

We have a quadrilateral inscribed in a circle (a cyclic quadrilateral).....whenever this is so....the opposite angles in the quadrilateral are supplementary (the sum to 180°)

So

A + C = 180

A + 101 = 180 subtract 101 from both sides

A = 79°

Smillarly

B + D = 180

B + 68 = 180

B = 180 - 68

B = 112°

CPhill Feb 26, 2019

#2**+1 **

These are all answered so differently. How am I supposed to know which formula to use for each problem?

RainbowPanda
Feb 26, 2019

#3**+2 **

Second one

Notice that angle Q intercepts arc PSR

And the measure of this arc= 137 + 41 = 178°

And because angle Q is an inscribed angle intercepting this arc...it measures (1/2)(arc PSR) = (1/2)(178) = 89°

We have a cyclic quadrilateral....R is supplemental to 57° = 180 - 57 = 123°

And S is supplemental to Q = 180 - 89 = 91°

CPhill Feb 26, 2019