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

#2**+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**+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**+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