The shaded triangle formed by points D, E and C is equilateral. If angle EAB is 40°, then what is the value of angle ABC?

Answer

To find the value of angle ABC, we first acknowledge the properties of the triangle and the given information. 1. The angle EAB is given as 40°. 2. The triangle DEC (the shaded triangle) is equilateral, which means all its angles are equal to 60°. 3. In triangle EAB, we can find angle ABE because we know that the sum of angles in any triangle is 180°. Now let’s analyze triangle EAB: - Angle AEB = 60° (Since triangle DEC is equilateral and angle EAB is part of this triangle) Using the angles of triangle EAB: - Angle EAB + Angle ABE + Angle AEB = 180° - 40° + Angle ABE + 60° = 180° - Angle ABE = 180° - 100° = 80° Now we need to find angle ABC. Since angle ABC is the same as angle ABE (because DE is parallel to line AB and they are alternate interior angles), we have: - Angle ABC = Angle ABE = 80° Thus, the value of angle ABC is 80°.