Question

the angles or the paralelogram.
8. Find the measure of each angle of a parallelogram, if one of its angles is
30° less than twice the smallest angle.​

Answer 1

Step-by-step explanation:

In a parallelogram , sum of the four angles =360.

opp. angles of parallelogram are same.

Suppose the angles are x and y

x+y=180

given that x = 2y - 30

180-y=2y- 30

y =70

x =110

Answer 2

$\large{\underline{\rm{\purple{\bf{Question:-}}}}}$

Find the measure of each angle of a parallelogram, if one of its angles is  30° less than twice the smallest angle.​

$\large{\underline{\rm{\purple{\bf{Given:-}}}}}$

Measure of one angle of a parallelogram less than twice the smallest angle = 30°

$\large{\underline{\rm{\purple{\bf{To \: Find:-}}}}}$

The measure of each angle.

$\large{\underline{\rm{\purple{\bf{Solution:-}}}}}$

We know that, the total degree of a triangle is 180°

In a parallelogram opposite angles are equal and the adjacent angles are supplementary.

Given that, one of the angle is 30° less than twice the smallest angle.

Let us consider x and y as the adjacent angles of the parallelogram, let x > y

We know that, $\sf x=2y-30$

$\sf x+y=180$

$\implies \sf 2y-30+y=180$

$\implies \sf 3y-30=180$

$\implies \sf 3y=180+30$

$\implies \sf 3y=210$

Now, finding the value of y

$\implies \sf y=\dfrac{210}{3}$

$\implies \sf y=70^{o}$

Next, substituting the value of  y in the equation x + y = 180

We have,

$\sf x+70=180$

Finding x,

$\implies \sf x=180-70$

$\implies \sf x=110^{o}$

Therefore, the angles of the parallelogram are 110°, 70°, 110°, 70°