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Quadrilateral ABCD  is inscribed in this circle.

 

What is the measure of  ∠A ?

Enter your answer in the box.

___°

​ Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?

 

Enter your answer in the box.

m∠A= __°

Guest Feb 23, 2018

Best Answer 

 #2
avatar+12735 
+1

The second one    (the arc degrees intercepted by an inscribed angle is equal to TWICE the angle)

  The two angles cover the complete 360 degrees of the triangle in their arcs

 

soooo     360 = 2 ( 3x+1    +   2x+9  )

              180 = 5x +10

                 170 = 5x        x = 170/5 = 34  degrees

 

a = 2(34) + 9 = 77 degrees 

ElectricPavlov  Feb 23, 2018
 #1
avatar+12735 
+1

First one

Inscribed angles are 1/2 of the arc that they cover

  the 121 degree angle covers   121 x2 = 242 degreees of the circle......

   the other angle covers  360 - 242 = 118 degrees 

     so the angle in question = 118/2 = 59 degrees

ElectricPavlov  Feb 23, 2018
 #2
avatar+12735 
+1
Best Answer

The second one    (the arc degrees intercepted by an inscribed angle is equal to TWICE the angle)

  The two angles cover the complete 360 degrees of the triangle in their arcs

 

soooo     360 = 2 ( 3x+1    +   2x+9  )

              180 = 5x +10

                 170 = 5x        x = 170/5 = 34  degrees

 

a = 2(34) + 9 = 77 degrees 

ElectricPavlov  Feb 23, 2018

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