Question

Find the unknown angle:​

Answer 1

w = 72°

x = 36°

2x = 72°

3x = 108°

y = 72°

z = 108°

Explanation:

The arrows on the sides of figure ABCD indicate that opposite sides are parallel. Therefore, ABCD is a parallelogram.

In a parallelogram:

• Opposite angles are equal.
• Interior angles sum to 360°.
• Adjacent angles are supplementary (sum to 180°).

As adjacent angles sum to 180°:

⇒ m∠A + m∠B = 180°

⇒ 3x + 2x = 180°

⇒ 5x = 180°

⇒ x = 36°

Therefore:

⇒ m∠A = 3(36) = 108°

⇒ m∠B = 2(36) = 72°

As opposite angles are equal:

⇒ y = m∠D = m∠B = 72°

⇒ z = m∠BCD = m∠A = 108°

Angles on a straight line sum to 180°:

⇒ z + w = 180°

⇒ 108° + w = 180°

⇒ w = 72°

Answer 2

• x = 36°, y = 72°, z = 108°, w = 72°

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Given is the parallelogram.

Properties:

• Adjacent angles are supplementary;
• Opposite angles are congruent.

Solve the following:

• 2x + 3x = 180
• 5x = 180
• x = 180/5
• x = 36

• y = 2x = 2*36 = 72
• z = 3x = 3*36 = 108
• w = 180 - z = 180 - 108 = 72