Question

The adjacent angles of a parallelogram are (8x + 1)deg and(16x - 13)deg . Find the measures of the angles.​

Answer 1

Given that, the adjacent angles of a parallelogram are (8x + 1)° and (16x – 13)°.

We’ll have to find the measure of all the angles in that parallelogram.

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Let the parallelogram be PQRS, wherein :

• $\angle$P = (8x + 1)°
• $\angle$Q = (16x – 13)°

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In a parallelogram, opposite angles are equal, so :

• $\angle$R = $\angle$P
• $\angle$S = $\angle$Q

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We know that, adjacent angles in a parallelogram are supplementary.

• $\angle$P + $\angle$Q = 180°

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Now, substituting and finding the value of x :

⟹$~~\sf (8x + 1)\degree+ (16x – 13)\degree= 180\degree$

⟹$\sf ~~8x +1+16x-13 = 180\degree$

⟹$\sf ~~8x + 16x + 1 - 13 = 180\degree$

⟹$\sf ~~24x - 12 = 180\degree$

⟹$\sf ~~ 24x = 180+12$

⟹$\sf ~~ 24x = 192$

⟹$\sf ~~ x=192/24$

⟹$\sf ~~x = 8\degree$

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Substituting the value of x in the angles :

• $\angle$P = $\angle$R=(8x+1)°

⟹$\sf ~~(8x+1)\degree$

⟹$\sf ~~[8(8)+1]\degree$

⟹$\sf ~~(64+1)$

⟹$\sf ~~65\degree$

• $\angle$Q=$\angle$S=(16x–13)°

⟹$\sf ~~(16x–13)\degree$

⟹$\sf ~~ [16(8)-13]\degree$

⟹$\sf ~~ (128-13)\degree$

⟹$\sf ~~115\degree$

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Therefore, the angles of the parallelogram PQRS are 65°, 115°, 65° and 115°.