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The isosceles trapezoid ABDE is part of an isosceles triangle ACE. Find the measure of the vertex angle of ACE

A: 130
B: 60
C: 65
D: 50

The isosceles trapezoid ABDE is part of an isosceles triangle ACE Find the measure of the vertex angle of ACE A 130 B 60 C 65 D 50 class=

Respuesta :

carlosego
You can solve this problem by folllowing the steps below:
 
  1. Draw a segment from the point C to the line AE, as you can see in the figure attached.
 2. You have now two equal right trapezoids, then: m∠ABG=m∠EDG.
 3. m∠ACE=m∠EDG
 3. The sum of the interior angles of the trapezoid is 360º.
 4. Then, you have:
 
 m∠EDG+m∠D+m∠G+m∠F=360º
 
 m∠D=115º
 m∠G=90º
 m∠F=90º
 
 5. When you clear m∠EDG, you obtain:
 
 m∠EDG=360º-m∠D-m∠G-m∠F
 m∠EDG=360º-115º-90º-90º
 m∠EDG=65º
 
 6. Therefore:
 
 m∠ACE=m∠EDG
 m∠ACE=65º
 
 The answer is: C.65º
Ver imagen carlosego

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