Q. 75.0( 2 Votes )

# Two opposite angles of a parallelogram are (3x-2)o and (50-x)o. The measures of all its angles areA. 97°, 83°, 97°, 83°B. 37°, 143°, 37°, 143°C. 76°, 104°, 76°, 104°D. none of these

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°.

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