Question

In a parallelogram ABCD angle A=3x+23,angle B=2x+17then angle D =​

Answer 1

Answer:

The angle ∠D=73°

Step-by-step explanation:

Concept:

Adjacent angles of a parallelogram are supplementary

Given:

∠A=3x+23° and ∠B=2x+17°

Then,

∠A + ∠B= 180°

(3x+23°)+(2x+17°)=180°

5x+40°=180°

5x=180°- 40°

5x=140°

$\implies$x=28°

Also,

∠A + ∠D= 180°

(3(28°)+23°)+∠D=180°

(84°+23°)+∠D=180°

(107°)+∠D=180°

∠D=180° - 107°

$\implies$∠D=73°

Answer 2

Answer: The Angle ∠D=73°

Step-by-step explanation:

Given,

The angles in a parrallelogram are ∠A=3x+23° and ∠B=2x+17°

we know that In a parralelogram that the adjacent angles of a parralelogram are supplementary

so, ∠A+∠B=180°

  substitute the values of ∠A and ∠B in the above

then 3x+23°+2x+17°=180°

        5x+40°=180°

        5x=140°

        x=28°

Now we can obtain the values of ∠A and ∠B values as we know the value of x

∠A=3(28)+23=107°

∠B=2(28)+17=73°

Therefore,∠A+∠D=180°

      107°+∠D=180°

        ∠D=73°

Therefore the angle of D in a parallelogram ABCD is 73°