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avatar+2448 

Do I just add up the measurements that are already there first?

 Feb 26, 2019
 #1
avatar+101871 
+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°

 

cool cool cool

 Feb 26, 2019
 #2
avatar+2448 
+1

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

RainbowPanda  Feb 26, 2019
 #4
avatar+101871 
+2

We are only really using two theorems here

 

1)   Opposite angles in a cyclic quadrilateral  sum to 180°

 

2)  The measure of an inscribed angle =  (1/2) the measure of the arc it intercepts

 

 

 

cool cool cool

CPhill  Feb 26, 2019
 #3
avatar+101871 
+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°

 

 

cool cool cool

 Feb 26, 2019

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