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In the diagram, AB is parallel to DC and ACE is a straight line. What is the value of x?

 

 Nov 17, 2019
 #1
avatar+212 
+2

Angle ACB = 180 - 105 = 75 (LINEAR PAIR POSTULATE)

 

Angle BAC = 180 - (75 + 75) = 30 (TRIANGLE SUM THEOREM)

 

Angle BAD + Angle ACD = 180 (SAME SIDE INTERIOR ANGLES THEOREM)

 

Angle  BAD = Angle BAC + Angle CAD (ANGLE ADDITION POSTULATE)

 

115 + 30 + x = 180 

145 + x = 180 

x = 180 - 145 

x = 35 degrees

 Nov 17, 2019
 #2
avatar+105411 
+2

Angle ACB  is supplemental to angle ECB....so its measure =  180 - 105 = 75°

 

So triangle ACB  is isosceles with angle  BAC   = 30°

 

And angles BAC  and ACD  are alternate interior angles....so  angle ACD  = 30°

 

So angle  CAD  = x =   180  - 115 - 30 =   35°

 

 

cool cool cool

 Nov 17, 2019

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