Question

In the parallelogram PQRS ∠P = 3x – 10°, ∠Q = 2x + 20°. ∴ The measure of x is ______.

Options

• 30°

• 34°

• 28°

• 36°

Answer 1

In the parallelogram PQRS ∠P = 3x – 10°, ∠Q = 2x + 20°. ∴ The measure of x is 34°.

Explanation:

Step 1: Use the property of a parallelogram

In a parallelogram, consecutive angles are supplementary, meaning their sum is 180°.

Angles P and Q are consecutive angles, so we can set up the following equation:

∠P + ∠Q = 180°

(3x – 10°) + (2x + 20°) = 180°

Step 2: Solve for x

Combine the like terms on the left side of the equation:

3x + 2x – 10° + 20° = 180°

5x + 10° = 180°

Subtract 10° from both sides:

5x = 180° – 10°

5x = 170°

Divide both sides by 5:

x = `170^circ/5`

x = 34°