Mathematics
Grade9
Easy

Question

If angle A B E equals 100 degree, then the measure of angle D A E = _____________.

  1. 80°
  2. 40°
  3. 100°
  4. 20°

hintHint:

properties of rectangle
opposite sides are parallel and equal to each other.
Each interior angle is equal to 90 degrees.
The sum of all the interior angles is equal to 360 degrees.
diagonals bisect each other.
Both the diagonals have the same length.

The correct answer is: 40°


    The diagonals of a rectangle are equal ( diagonals bisect each other)
    So, AB = BD = BC = BE
    In isosceles triangle triangle A B E, AB = BE
    angle ABE plus angle BAE plus angle BEA equals 180 degree space
angle BAE plus angle BAE equals 180 degree minus angle ABE space space space space
space space space space space left square bracket Angles space opposite space to space equal space sides space are space equal right square bracket
angle BAE plus angle BAE equals 180 degree minus angle 100 to the power of O
2 angle BAE space equals space 80 degree
angle BAE space equals space 40 degree space i s space t h e space a n s w e r
    So, angle DAE space equals space 40 degree

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