Question

the adjacent angels of a pallelogram are (3x-4)degree and (2x-1)degree find all the measures of all angles of pallelogram
explain by giving method ​

Answer 1

Answer:

4x-2+6x-8 = 360

10x - 10 = 360

x = 35

Step-by-step explanation:

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Answer 2

To Find:-

• The measure of all angles

Given:-

• The adjacent angles of a Parallelogram is (3x-4)° and (2x-1)°

Solution:-

Let ABCD be a Parallelogram and ∠A = ( 3x - 4 )° ; ∠B = ( 2x - 1 )°

Now,

• First, value of x

( 3x - 4 ) + ( 2x - 1 ) = 180° ( adjacent angles are supplementary )

step-by-step explanation:

⟹ 3x - 4 + 2x - 1 = 180°

⟹ 3x + 2x = 180 + 1 + 4

⟹ 5x = 185

⟹ x = 185/5

⟹ x = 37

The measure of the angles

• ∠A ( 3x - 4 )

⟹ 3 × 37 - 4

⟹ 111 - 4

⟹ 107°

• ∠B ( 2x - 1 )

⟹ 2 × 37 - 1

⟹ 74 - 1

⟹ 73°

The angles are:-

∠A = ∠C = 107° ( opposite angles)

∠B = ∠D = 73° ( opposite angles )

Now, Verification

We know that a Parallelogram measures 360°. So,

∠A + ∠B + ∠C + ∠D = 360°

⟹ 107° + 73° + 107° + 73° = 360°

⟹ 180° + 180° = 360°

⟹ 360° = 360°

L.H.S = R.H.S

Hence, Proved