Question

find the measure of all the angels of a parallelogram, if one angle is 36° less than the twice the smallest angle​

Answer 1

$\displaystyle\huge\purple{\underline{\underline{Solution}}}$

In case of a parallelogram opposite angles are equal and the adjacent angles are supplementary . Let x and y are the adjacent angles of the parallelogram . Let x > y .

$\displaystyle\huge\red{\underline{\underline{Given}}}$

One of the angle is 36° less than twice the smallest angle .

That is x = 2y - 36

$\displaystyle\huge\orange{\underline{\underline{To\:Find}}}$

Measure of all angles

$\displaystyle\huge\blue{\underline{\underline{Answer}}}$

Since x + y = 180 , we have

2y - 36 + y = 180

3y - 36 = 180

3y = 180 + 36

3y = 216

y = $\dfrac{216}{3}$

y = 72

Substituting the value of y in x + y = 180 .

Thus we have ,

x + 36 = 180

x = 180 - 36

x = 144

Thus the angles are 144 , 72 , 144 , 72 .

Answer 2

$\red{Given\::-}$

• One angle of the parallelogram is 36° less than twice the smallest angle

$\orange{To\:Find\::-}$

• Measure of all angles of a parallelogram

$\purple{Solution\::-}$

W.K.T

• Sum of adjacent sides of parallelogram = 180°

Let,

• The adjacent angle be x

⇒ x + 2x - 36 = 180°

⇒ 3x = 180° + 36°

⇒ 3x = 216

⇒ x = $\dfrac{216}{3}$

⇒ x = 72

◆ Putting value of y in x + y = 180 .

⇒ x + 36 = 180

⇒ x = 180 - 36

⇒ x = 144

☀️ Angles are 144, 72, 144, 72