Question

Measure of one angle of a parallelogram is 100°.find the other three angles

Answer 1

As per data given in the question,

We have to determine the all the angles of parallelogram.

As we know that,

• In parallelogram, opposite angles are equal.
• Sum of all angles of parallelogram = 360 - degree

So, from given data,

We have,

One angle of parallelogram = $100^0$

So, opposite angle which will be opposite to $100^0$ will be of $100^0$.

As we know that,

Sum of all angles of parallelogram = $360^0$

So,

Let the other two angles are of $x^0$

So,

$100^0+100^0+x^0+x^0=360^0\\=>2x^0=360^0-200^0\\=>2x^0=160^0\\=>x^0=\frac{160^0}{2}\\=>x^0=80^0$

Hence, all four angles of parallelogram will be $100^0,100^0,80^0\:and\:80^0$ respectively.

Answer 2

• As per the data given in the question, we have to find the value of the parallelograms other three angles.

           Given data:- Masure of one angle of a parallelogram is $100$ °

           To find:- Value of other three angles=?

           Solution:-

• We know that Opposite sides are parallel and equal to each other of a parallelogram.
• There are some properties of a parallelogram are as follows,

1. The Opposite sides are parallel.
2. Opposite sides are congruent.
3. Opposite angles are congruent.  
4. Same-Side interior angles (consecutive angles) are supplementary.

       Therefore,

               $let\ ABCD \ is\ parallelogram.\\And\ angle\ B= 100 degree.\\ \ B= \ D \\=100\ degree\\\ A+B=180\\ A + 100\ degree\\= 180 \ degree\\A=180-100\ degreeA= 80 \ degree.$

Hence we will get the angle $100,180 \ and \ 80\ degree.$