Question

1. ∠1 and ∠2 are supplementary and ∠1 ≅ ∠2. which one of these statements will always be true? ∠1 and ∠2 are complementary angles; ∠1 and ∠2 are adjacent angles; ∠1 and ∠2 are right angles; ∠1 and ∠2 are vertical angles.

Explanation:

Step1: Recall supplementary angles

Supplementary angles sum to \(180^\circ\), so \(\angle1 + \angle2 = 180^\circ\).

Step2: Use \(\angle1\cong\angle2\) (equal measure)

Let \(m\angle1 = m\angle2 = x\). Then \(x + x = 180^\circ\), so \(2x = 180^\circ\).

Step3: Solve for \(x\)

Divide both sides by 2: \(x=\frac{180^\circ}{2}=90^\circ\). So each angle is \(90^\circ\) (a right angle).

Step4: Analyze other options

• Complementary angles sum to \(90^\circ\), not \(180^\circ\), so first option is false.
• Adjacent angles share a side/vertex, but supplementary angles don't have to be adjacent, so second option is false.
• Vertical angles are equal but supplementary only if they're \(90^\circ\), but this isn't always true for vertical angles, so fourth option is false.

Answer:

\(\angle1\) and \(\angle2\) are right angles