Question

calculate the value of x in each of the following figures

plz the this one answer plz ​

Answer 1

Answer:

• 75° is the measure of ∠x.

Step-by-step explanation:

We have AB║CD.

Given:

∠BAE = 60°

∠DCE = 45°

To find:

∠x = ?

Solution:

∠DAE = ∠AED = 60°

• [∵ Alternate interior angles are equal]

Now, in ΔDEC:

∠DCE + ∠ADE + x° = 180°

• [∵ Angle sum property]

⇒ 45° + 60° + x° = 180°

⇒ 105° + x = 180°

⇒ x° = 180° - 105°

⇒ x° = 75°

∴ The measure of ∠x = 75°.

Verification:

• Angle sum property:

∠x + ∠DCE + ∠EDC = 180°

⇒ 75° + 45° + 60° = 180°

⇒ 120° + 60° = 180°

⇒ 180° = 180°

Answer 2

Answer: 75 Degree

Sol. [All angles of a triangle = 180 degree]

As, all angles of a triangle when added, give the result 180 Degree.

      Given, AB || CD and AB and AD make the angle of 60 degree. Hence ED and DC = 60 degree

If, EC and DC = 45 degree, and ED and DC = 60 degree, then

x = 180 - (45 + 60)

=> x = 180 - 105

=> x = 75

ANS) 75 Degree

Hope this helped ya : )