Question

Assertion: If the opposite angles of a parallelogram are (3x – 6)° and (50 – x)°, then measure of the angles is 36°.

Reason: Opposite angles of a parallelogram are equal.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

Both A and R are true and R is the correct reason for A.

Explanation:

Step 1: Set the expressions for the angles equal to each other.

Since the opposite angles are equal, we can write the equation:

(3x – 6)° = (50 – x)°

Step 2: Solve for x.

Add x to both sides:

4x – 6 = 50

Add 6 to both sides:

4x = 56

Divide both sides by 4:

x = 14

Step 3: Find the measure of the angles.

Substitute the value of x back into either expression.

Using (3x – 6)°:

3(14) – 6

= 42 – 6

= 36°

Using (50 – x)°: 

50 – 14 = 36°

Both expressions give the same result, confirming that the measure of the angles is 36°.

Therefore, the Assertion is true.