Question

1.) In a quadrilateral PQRS, P = 60°, ZQ = 70° and ZR = 120°. Find angle S.

2.) The angles of a quadrilateral are in the ratio of 2 : 3:4:6. Find its angles.

3.) Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.​

Answer 1

Answer:

1 . In a quadrilateral PQRS

given, P= 60°, Q= 70° and R=120°

Let the side S be x

as we know, Sum of all the interior angles of a quadrilateral is 360°

Therefore,

60+70+120+x=360°

250x= 360°

x= 360÷250

2.Let the 1st angle be 2x

2nd angle be 3x

3rd angle be 4x

4th angle be 6x

sun of interior angles of a quadrilateral=360°

2x+3x+4x+6x= 360°

15x=360°

x=360°=15

x=24°

so the 1st angle = 2x

= 2×24

=48°

2nd angle=3x=3×24=72°

3rd angle =4x=4×24=96°

4th angle= 6x =6×24= 144°

Verification

sum of all the interior angles of a quadrilateral=360°

48°+72°+96°+144°= 360°

360°=360°

therefore, it is verified