How big is angle AED?
A normal-level "Angle" problem.Whenever a square meets an equilateral triangle, start from the 30° left over between 90° and 60°. After that it is just the base angles of an isosceles triangle.
GivenInside square ABCD, an equilateral triangle DCE is drawn on side DC.
Hints
- Pull out triangle ADE, the one containing the angle we want. AD is a side of the square and DE is a side of the equilateral triangle — and that triangle was built on DC, another side of the square. So AD = DE: it is isosceles.
- Next, the angle at D. It is a corner of the square, so angle ADC = 90°.
- Sitting inside that 90° is the equilateral triangle's corner: angle EDC = 60°.
- So the angle left between them is 90 − 60 = 30°. That is the apex angle of the isosceles triangle ADE.
- In an isosceles triangle the two base angles are equal. The three angles total 180°, so the two base angles share 180 − 30 = 150°: 150 ÷ 2 = 75°.
Answer 75度
More "Angle" problems
- How big is angle x?
- How many degrees is angle x?
- What is A＋B＋C＋D＋E?
- How big is angle BIC?
- How many degrees is angle x?
- How many degrees is angle x?