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The value of ∠4 is 45° .

Step-by-step explanation:

Given that , ∠4 = x + 30 ° & ∠2 = 2x + 15 .We need to find the measure of ∠4 . So from the figure we can see that , ∠2 & ∠4 are corresponding angles .So they will be equal.

⇒ ∠2 = ∠4 [ Corresponding angles ]

⇒ x + 30° = 2x + 15°

⇒ 2x - x = 30° - 15°

⇒ x = 15°

Hence the value of x is 15°

⇒ ∠4 = x + 30°

⇒ ∠4 = 15° + 30°

⇒ ∠4 = 45°