Question

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

Answer 1

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