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In the figure shown, ABCD is a square and CDE is equilateral. What is the degree measure of CBE?

 

 Feb 7, 2022
 #1
avatar+36 
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We know that since the angle of a square is 90 degrees, and an equilateral triangle has an angle of 60. So, we know that BEC = 90-60 = 30. 

 

CE = CD (because it is an equilateral triangle)

CD = CB (because it is a square)

CE = CB

Thus, CBE = CEB

 

Since a triangle's angles add up to 180, we know:

 

CBE + CEB + 30 = 180

CBE + CEB = 150

Since CBE and CEB are equal, they both equal 150/2 = 75

 

This means that Angle CBE = 75 degrees.

 

Let me know if I did anything wrong!

 Feb 7, 2022
edited by InhumanCalculator  Feb 7, 2022
 #2
avatar+2440 
+1

We know that \(\angle BCE =30\). We know that \(BC\) and \(CE\) are the same length, so\(\triangle{CEB}\) is isosceles. This means that \(\angle CBE=\color{brown}\boxed{75^{\circ}}\)

 Feb 7, 2022

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