Question

in a parallelogram find the sum of all angle if one of its angle mease 15 less than twice the smallest angle​

Answer 1

Question :-

in a parallelogram find the sum of all angle if one of its angle mease 15 less than twice the smallest angle.

Given :-

• Smallest angle = x

• Other angle = 2x - 15

To Find :-

• The sum of all angles.

Solution :-

According to the question, smallest number should be x and the other number should be 2x - 15. We know that in a parallelogram, there are 4 sides that adds up to 360°.

Therefore, x + x + (2x - 15) + (2x - 15) = 360°

⇒x + x + (2x - 15) + (2x - 15) = 360°

⇒x + x + 2x - 15 + 2x - 15 = 360°

⇒2x + 2x + 2x - 15 - 15 = 360°

⇒6x - 30 = 360°

⇒6x = 360 + 30

⇒6x = 390

⇒x = 390/6

⇒x = 65°

Therefore, value of smallest angle measures 65°.

★ The other angle measures :-

⇒2x - 15

⇒2 × 65 - 15

⇒130 - 15

⇒115°

Therefore, the other angle measures 115°.

★ We know that in a parallelogram, opposite angles are equal. Therefore, the 4 angles measures : 65° , 115° , 65° and 115°.

Joyful learning!!!⛅