Question

E is mid-point of side BC of parallelogram ABCD such that CD : AD = 1 : 2. If ∠BAE = 40°, then ∠ADE equals ____ ​

Answer 1

Answer:

50

Step-by-step explanation:

Parallelogram ABCD => AD = BC

CD : AD = 1 : 2 => CD= 1/2AD = 1/2BC

E is mid-point of side BC of parallelogram ABCD => EC = EB = 1/2BC

=> CD = EC => ΔDCE is isosceles triangles (1)

=> ∠DAE = ∠BAE = ∠AEB = 40°

∠BAD = ∠BAE + ∠DAE = 40°+40°=80°

Consecutive angles are supplementary ∠BAD + ∠ABC = 180°

=> ∠ABC=180°-80°=100°

Opposite angels are congruent

∠ABC = ∠ADC = 100° (2)

∠BAD = ∠DCB = 80°

A triangle's angles add up to 180 degrees

ΔDCE = ∠CDE + ∠DCE + ∠CED = 180°

∠CDE + ∠CED  = 180° - ∠DCE = 180 ° - 80° = 100°

(1) ΔDCE is isosceles triangles. An isosceles triangle is a triangle with (at least) two equal sides. This property is equivalent to two angles of the triangle being equal.

=> ∠CDE = ∠DCE  = 50°

(2) ∠ADC  = 100° =  ∠ADE + ∠CDE = ∠ADE + 50°

=> ∠ADE = 100°-50°=50°