Question

7. Two opposite angles of a parallelogram are (3x - 2) and (50 - x)". The measures of all
angles are
(a) 97, 83, 97, 83
(b) 37. 143, 37", 143
(c) 769. 104, 76, 104
(d) none of these​

Answer 1

we know that

opposite angle of parallelogram are equal

so

3x - 2 = 50 - X

4x = 52

x = 13

opposite angle are 41 and 37

other two angle are 139 and 143

Answer 2

Option (b) is right,

37°, 143°, 37°, 143°.

Explanation:

It is stated that,

One of the angle of the parallelogram measures (3x-2) and its opposite angle measures (50-x)

Let us assume ABCD is a parallelogram.

Then we get the angles_

∠ABC

∠BCD

∠CDB

∠DAB

Let, ∠ABC = (3X-2)

∴ ∠CDB = (50-X)

According to the problem,

∠ABC = ∠CDB [∵ The opposite angles of a parallelogram are equal.]

∴ (3x-2) = (50-x)

⇒ 3x+x = 50+2

⇒ 4x = 52

⇒ x = 52/4

⇒ x = 13

∴∠ABC = ∠CDB = (50-13)° [∵Opposite angles are equal.]

                           = 37°

∠BCD = 180° - ∠ ABC

[∵co-interior angles and sum of the co-interior angle is 180°.]

∴∠BCD = 180°-37°

            = 143°

∴∠BCD = ∠DAB = 143°  [∵Opposite angles of a parallelogram are equal.]

Hence, we get_

∠ABC = 37°

∠BCD = 143°

∠CDB = 37°

∠DAB = 143°

∴ Option (b) is right_ 37°, 143°, 37°, 143°.

#answerwithquality

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