Two unequal angles of a parallelogram are in the ratio 2 : 3 Find all its angles in degrees

Text Solution

Solution : Let `∠A=2x` and `∠B=3x`<br>Now,<br>`∠A+∠B=180^@`[ Co-interior angles are supplementary ]<br>⇒`2x+3x=180^@`<br>⇒ `5x=180^@`<br>⇒ `x= 180^@/5`<br>⇒ `x=36^@`<br>∴ `'∠A=2×36^@=72^@` and `∠B=3×36^@`<br>=`108^@`<br>We know opposite angles of a parallelogram are equal.<br>∴ `/_A=/_C=72^@`<br>And `/_B=/_D=108^@`

Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees .

Let `∠`A = 2x and `∠`B = 3x

Now,

`∠`A + `∠`B = 180°                           [Co-interior angles are supplementary]

2x + 3x -180°                              [ AD || BC and AB is the transversal]

⇒ 5x =180°

⇒ x = `(180°)/ 5` = 36°

∴`∠`A = 2 ´ 36° = 72°

`∠` B = 3´ 36° = 108°

Now,

`∠`A = `∠`C = 72°                           [Opposite side angles of a parallelogram are equal]

`∠`B = `∠`D =108°

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