Answer: Angle AEF is 90°
Step by step explanation:
Given: CDF is a straight line, so the three angles that meet at D must total 180°
Given: ABCD is a square. By definition, all angles are 90° so CDA is 90°
Given: Triangle DEF is equilateral. By definition, all the angles are equal to 60° so angle EDF is 60°
Add angles EDF and ADC and subtract from 180
180 -(90 + 60) = 30
Given: Triangle ADE is iscoceles, so the angles opposite the given equal sides AE and AD are equal.
Angles AED and ADE are equal.
AED = 30°
Angle DEF of the equilateral triangle is 60°
The measure of angle AEF is the sum of angles AED + DEF 30 + 60 = 90.
Therefore the measure of angle AEF is 90°
