In parallelogram ABCD, the angle is C = 40 degrees. Point E lies on side BC, and the angle BAE = 20 degrees,

| November 29, 2020 | education

In parallelogram ABCD, the angle is C = 40 degrees. Point E lies on side BC, and the angle BAE = 20 degrees, EC = 2 cm, AB = 10 cm. Find AD

1) by the property of a parallelogram, the angle c and the angle d add up to 180 degrees. Hence the angle d = 180-40 = 140 degrees.
2) by the properties of the parallelogram, its opposite angles are equal. Angle d = angle c = 140 deg.
3) consider the treug ave:
– the sum of the angles of the triangle is 180 degrees. This means the angle wea is 180-140-20 = 20 degrees.
– triangle ave angles at the base are equal (angle a = angle e = 20), which means it is isosceles.
-in isosceles treug. the sides are equal. AB = BE = 10.
4) by the properties of the parallelogram, the opposite sides are equal. BC = ad.
5) BC = BE + EC = 10 + 2 = 12. T.E.Ad = 12.
Answer: 12



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