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

Guest Feb 7, 2022

#1**+1 **

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!

InhumanCalculator Feb 7, 2022

#2**+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 \(\angle CBE=\color{brown}\boxed{75^{\circ}}\)

BuilderBoi Feb 7, 2022