Question

The adjacent angles of parallelogram PQRS are (2x−13)° and (x+4)°. Find the measure of all the angles of the parallelogram.

Answer 1

Here it is given that adjacent angles are (2x-13)° and (x+4)°.

We know that adjacent angles of a parallelogram are supplementary.

So,

This gives (2x-13)°+(x+4)°=180°

Simplifying, we get (2x+x-13+4)°=180°

Thus,

3x-9=180

3x=189

x=189/3

x=63°.

Now

Angle 1 = 2x-13= (2× 63) - 13 = 126-13= 113°.

Angle 2 = x+4 = 63+4= 67°.

Now we know that opposite angles are equal in a parallelogram.

Therefore angles are 67, 113, 67, 113.

Answer 2

Answer:

Step-by-step explanation:

SUM OF THE ADJACENT ANFGLES

∠P + ∠ R =180°

2x-13+x+4=180

3x=189

x=63

∠P=2x-13=2*63-13=113°

∠R=∠P=113°

∠S =∠Q=180-113=67°