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In a straight line, all angles sum up to 180°

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[tex]\hookrightarrow \sf x +\dfrac{1}{4} x = 180[/tex]

[tex]\hookrightarrow \sf \dfrac{4x}{4} +\dfrac{1}{4} x = 180[/tex]

[tex]\hookrightarrow \sf \dfrac{4x+x}{4} = 180[/tex]

[tex]\hookrightarrow \sf 4x+x= 180(4)[/tex]

[tex]\hookrightarrow \sf 5x= 720[/tex]

[tex]\sf \hookrightarrow x = 144[/tex]

Answer:

x = 144°

Step-by-step explanation:

Since the larger line is a straight line, ∠1 and ∠2 are a linear pair. A linear pair is such a pair where two angles sum up to 180°.

⇒ ∠A + ∠B = 180°

Substitute the measure of ∠A and ∠B

⇒ x + x/4 = 180°                                                                    [∠A = x; ∠B = x/4]

⇒ 4x/4 + x/4 = 180°                                                           [Rewrote x as 4x/4]

⇒ 5x/4 = 180°

Using cross multiplication

⇒ 5x = 180 × 4 = 720

⇒ x = 720/5 = 144°

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