Question

in a parallogram PQRS q=105 degree find all the other angle of the given parallogram

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Answer 1

Answer:

∠Q=105°

∠P=75°

∠R=75°

∠S=105°

Step-by-step explanation:

∠Q= 105°

As the opposite angles are equal in a parallelogram

∠Q=∠S

         105°=105°

As consecutive angles of a parallelogram are supplementary

∠Q+∠R=180°

         105°+x=180°

          x=180°-105°

          x=75°

As the opposite angles are equal in a parallelogram

∠R=∠P

        75°=75°

Answer 2

Answer

• Angle P = 75, Angle Q = 105, Angle R = 75, and Angle S = 105.

Given

• PQRS is a parallelogram.
• Angle Q = 105.

To Find

• All the angles of the given parallelogram.

Step By Step Explanation

We, know that ⤵

• In a parallelogram opposite angles are equal.

Hence, Angle Q = Angle S and Angle P = Angle R.

Angle Q = Angle S.

105 = Angle S.

Now, Sum of all the angle of a quadrilateral = 360.

Angle Q + Angle S + Angle P + Angle R = 360.

Substituting the value :

105 + 105 + Angle P + Angle R = 360.

210 + 2( Angle P ) = 360 [ Angle P = Angle R ]

2( Angle P ) = 360 - 210

Angle P = 150/2

Angle P = 75.

Angle P = Angle R

75 = Angle R.

Therefore, Angle P = 75, Angle Q = 105, Angle R = 75, and Angle S = 105.

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