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# ​ Not sure how to do these ones

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

Feb 26, 2019

#1
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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°   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
#4
+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   CPhill  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°   Feb 26, 2019