Lines DE and AB intersect at point C. What is the value of x?
12, 25, 38, 52

linear pair of angles

Solution:

Given, lines DE and AB intersect at point C.

From the figure,

∠ACE and ∠ECB form a straight angle.

Thus, the sum of angles is 180°.

∠ACE + ∠ECB = 180°

∠ACE = 2x + 2

∠ECB = 5x + 3

So, 2x + 2 + 5x + 3 = 180

⇒ 7x + 5 = 180

⇒ 7x = 180 - 5

⇒ 7x = 175

⇒ x = 175/7

⇒ x = 25

Therefore, the value of x is 25°.

Lines DE and AB intersect at point C. What is the value of x?

Summary:

Lines DE and AB intersect at point C. The value of x is 25°.

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