Question

Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. The measures of all its angles are 

A. 97°, 83°, 97°, 83° 

B. 37°, 143°, 37°, 143° 

C. 76°, 104°, 76°, 104° 

D. none of these

Answer 1

To Find: 

All angles of a parallelogram 

Given: Opposite angles are (3x - 2) and (50 - x) 

Diagram:

Let the parallelogram be ABCD, and opposite angles be ∠B and ∠D, such that∠A = (3x - 2)∠C = (50 - x) 

∠B = ∠D (Opposite angles of a parallelogram are equal) 

3x - 2 = 50 - x 

3x + x = 50 + 2 

4x = 52° 

x = 13° 

Putting the value of x, we get, 

∠B = 3(13) - 2 = 37°

∠D = 50 - 13 = 37°

Also. ∠A = ∠C 

(Opposite angles of a parallelogram are equal)By angle sum property of quadrilateral, 

∠A + ∠B + ∠C + ∠D = 360° 

37° + ∠A + 37° + ∠C = 360° 

2∠A + 74 =360°

2∠A = 286°

∠ A = 143° 

Hence, ∠A = ∠C =143° 

So, Angles of parallelogram is 37°, 143°, 37° and 143°.