Question

find all angles of the parallelogram ​

Answer 1

Ans

Angle B = 23

Angle D = 23

Angle A = 157

Angle C = 157

Answer 2

Step-by-step explanation:

Question:

Find all angles of the parallelogram .

Understanding:

As we know that a parallelogram is a quadrilateral whose opposite sides are parallel. So,the opposite angles of a parallelogram are equal.

Angles:

As we know that the opposite sides are equal so,

3x -13° = 2x +10°

Let's find the value of x.

=> 3x -13° = 2x +10°

(taking 2x to left side to make the equation in positive only)

=> 3x - 2x = 10 + 13

=> x = 23

Hence, the value of x is 23° .

Solution:

As we got that the value of x is 23.

So the angles are (by putting up the value of x).

1st angle:

=> 3x -13°

=> 3 x 23- 13

=> 69-13

=> 56 ans..

2nd angle:

Here also we will put the value of x as 23 only as the opposite angles of a parallelogram are equal.

=> 2x +10°

=> 2 x 23 +10

=>46+10

=>56 ans...

Hence, the angle 3x -13°(let it be a) measures 56°.

2x +10° (let it be b) measures 56°.

Other two angles are:

Sum of all the angles of a parallelogram is 360°.

Let both the angles be x.

By linear pair , this means the angle on same side sum would be equal to 180°.

180- Angle a = Angle x¹

180 - 56 =24

: x¹ measures 24°.

180- Angle b = Angle x²

180- 56 =24

: x² measures 24°.

All the angles are :

: 56 ,24, 56, 24.

Note:

Here x¹ and x² are taken to segregate both the angles are they both are taken as x only. As the opposite angles of a parallelogram are equal.

♣️ Hope it helps ♣️