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Quadrilateral ABCD  is inscribed in this circle.

What is the measure of  ∠A ?

___°

​ Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?

m∠A= __°

Feb 23, 2018

#2
+18055
+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

Feb 23, 2018

#1
+18055
+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

Feb 23, 2018
#2
+18055
+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