Question

In the given figure, ABCD is a parallelogram. Find the value of x

30
40
75
45​

Answer 1

We have:-

• A parallelogram ABCD with opposite angles A and C marked as 3x - 50° and x + 40°$.$

To FinD:-

• Value of x?

Solution:-

We know that in a parallelogram like ABCD, the opposite angles are equal in measure.

That means,

• ∠A = ∠C
• ∠B = ∠D

Hence,

⇒ 3x - 50° = x + 40°

⇒ 3x - x = 90°

⇒ 2x = 90°

⇒ x = 45°

Therefore:-

• The required value of x is 45° (D)

Note:

• The opposite angles of a parallelogram are equal in measure.
• The adjacent angles are supplementary and add upto 180°

Answer 2

Answer:

$\huge \bf \: given$

ABCD is a parallelogram in which a and c are given.

$\huge \bf \: to \: find$

Value of x

$\huge \bf \: solution$

As we know that in a parallelogram the measure of opposite sides are equal.

$\sf \angle \: a \: = \angle \: c$

$\sf \angle \: b \: = \angle \: d$

Therefore,

$\sf \implies \: 3x - 50 = x + 40$

$\sf \implies \: 3x - x = 50 + 40$

$\sf \implies \: 2x = 90$

$\sf \implies \: x \: = \dfrac{90}{2}$

$\sf \implies \: x = 45$

Let's verify

$\sf \implies3x - 50 = x + 40$

$\sf \implies \: 3 \times 45 - 50 = 45 + 40$

$\sf \implies \: 135 - 50 = 85$

$\sf \implies \: 85 = 85$

Hence the required answer is 45