Answer:
x=52.5
Step-by-step explanation:
Since ABCD is a parallelogram, B= ADC. So angle ADC is 105. Next since ED=AD, angle EAD=angle AED=x and ADE=75. So 2x+75=180, 2x=105, x=105/2
In parallelogram ABCD, m∠B = 105° then the value of x = 52.5
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Since ED ≈ AD,
∆AED is an isosceles triangle where ∠EAD and ∠AED has the same angle measurement
Now, ∠B = 105°, since ABCD is a parallelogram,
∠B = ∠D
∠ADC = 105°
∠ADE = 180°-105° = 75°
Now, ∠EAD + ∠AED+ ∠ADE = 180°
∠AED+∠AED+∠ADE = 180°
x+x+75°=180°
2x=180+75°
2x = 105°
x = 52.5°
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